Cho \(2\) tập hợp \(A = \left\{ {x \in \mathbb{R}|\left( {2x - {x^2}} \right)\left( {2{x^2} - 3x - 2} \right) = 0} \right\}\), \(B = \left\{ {x \in \mathbb{R}|\left( {2{x^2} + x} \right)\left( {3x - 12m} \right) = 0} \right\}\), với giá trị nào của \(m\) thì \(A = B\)?
Cho \(2\) tập hợp \(A = \left\{ {x \in \mathbb{R}|\left( {2x - {x^2}} \right)\left( {2{x^2} - 3x - 2} \right) = 0} \right\}\), \(B = \left\{ {x \in \mathbb{R}|\left( {2{x^2} + x} \right)\left( {3x - 12m} \right) = 0} \right\}\), với giá trị nào của \(m\) thì \(A = B\)?
Hãy suy nghĩ và trả lời câu hỏi trước khi xem đáp án
Ta có:
- \(A = \left\{ {x \in \mathbb{R}|\left( {2x - {x^2}} \right)\left( {2{x^2} - 3x - 2} \right) = 0} \right\}\)
- \(2x - x^2 = 0 \Leftrightarrow x(2-x) = 0 \Leftrightarrow x = 0 \vee x = 2\)
- \(2x^2 - 3x - 2 = 0 \Leftrightarrow (2x+1)(x-2) = 0 \Leftrightarrow x = -\frac{1}{2} \vee x = 2\)
Vậy \(A = \left\{ { - \frac{1}{2};0;2} \right\}\)
- \(B = \left\{ {x \in \mathbb{R}|\left( {2{x^2} + x} \right)\left( {3x - 12m} \right) = 0} \right\}\)
- \(2x^2 + x = 0 \Leftrightarrow x(2x+1) = 0 \Leftrightarrow x = 0 \vee x = -\frac{1}{2}\)
- \(3x - 12m = 0 \Leftrightarrow x = 4m\)
Vậy \(B = \left\{ {0; - \frac{1}{2};4m} \right\}\)
Để \(A = B\) thì \(4m = 2 \Leftrightarrow m = \frac{1}{2}\).
Câu hỏi liên quan
Read the following passage about urbanisation and mark the letter A, B, C, or D on your answer sheet to indicate the best answer to each of the following questions.
URBANISATION: A GROWING PHENOMENON
Urbanisation is the process through which cities grow, and higher populations begin to inhabit urban areas. This phenomenon has accelerated significantly over the past few decades due to various factors. One of the primary drivers is the search for better employment opportunities. In rural areas, job prospects are often limited to agriculture and small-scale industries, which might not provide sufficient income. Consequently, people migrate to cities seeking better livelihoods and living standards.
Additionally, urban areas offer more advanced educational facilities and healthcare services compared to rural regions. Many families move to cities to provide their children with higher-quality education and greater future opportunities. Access to hospitals and specialized medical services also attracts people to urban centers, especially in countries where rural healthcare is underdeveloped.
However, rapid urbanisation brings about several challenges. Overcrowding in cities can lead to inadequate housing, strained infrastructure, and increased pollution. The expansion of urban areas often results in the loss of green spaces and agricultural land, impacting food production and the environment. Governments and city planners must address these issues to ensure sustainable urban growth.
Despite these challenges, urbanisation has several positive aspects. Cities are often cultural melting pots, where diverse groups of people interact, leading to vibrant communities and innovation. The concentration of resources and talents in urban areas can drive economic growth and technological advancements.
Which of the following best paraphrases the underlined sentence in paragraph 2?
Mark the letter A, B, C or D on your answer sheet to indicate the best arrangement of utterances or sentences to make a meaningful exchange or text in each of the following questions from 13 to 17.
Dear Sam,
a. Our friendship taught me that different people can learn from each other. You helped me with math, and I helped you make new friends.
b. Remember when we had that big fight about the science project? I'm glad we found a way to work together.
c. Now, even though you moved to another city, we still talk every week. Distance cannot break our special bond.
d. I never thought we would become friends when we first met at school. You were so quiet, and I talked too much!
e. My parents were surprised when they saw how different we are, but now they always ask about you and your family.
Your friend forever,
LK
Điểm nào dưới đây thuộc đồ thị hàm số \(y=-{{x}^{3}}+3{{x}^{2}}-2\)?
Đảng Cộng sản Việt Nam là đội tiên phong của giai cấp nào?
Biểu thức nào sau đây là tam thức bậc hai
Cho 20 g chất rắn ở nhiệt độ vào 100 g chất lỏng ở Cân bằng nhiệt đạt được ơ Nhiệt dung riêng của chất rắn
Read the following passage and mark the letter A, B, C or D on your answer sheet to indicate the option that best fits each of the numbered blanks from 18 to 22.
Medical breakthroughs
After twenty years of research, scientists have finally succeeded in developing a vaccine for dengue, a viral disease found in tropical areas. (18)______. According to the World Health Organisation, each year between 50 and 100 million people develop dengue, (19 ______ . The commercialized vaccine can protect children in Asia and Latin America against the virus.
Artificial limbs have been around since ancient times, but no prosthetic has been as lifelike as the Bebionic small hand. (20) ______ . Electrical impulses triggered by the user's muscle movements (21)______. Specifically aimed at women and teenagers, the artificial hand enables the user to perform a range of activities previously unmanageable, such as using cutlery and riding a bike.
Good news for migraine patients - a special device is available. The battery-driven headband sits across the forehead and over the ears and has a self-adhesive electrode, which helps it stay in place. This electrode applies an electric current to the skin and tissue below the headband stimulating the nerves which are said to trigger the headaches. By wearing the headband for the recommended twenty minutes per day, (22)______.
- Ngày 5-6-1911, từ bến cảng Nhà Rồng, Nguyễn Tất Thành (sau này là Chủ tịch Hồ Chí Minh) rời Tổ quốc ra đi tìm đường cứu nước với thân phận người đầu bếp mang tên Văn Ba trên con tàu Amiral Latouche Tréville (tàu Đô đốc Latouche Tréville) rời cảng Sài Gòn đi Marseille. Đây là một trong 6 con tàu cỡ lớn chuyên chạy tuyến Pháp – Đông Dương của hãng Năm Sao.
Sau này, khi được hỏi về chuyến đi ngày 5-6-1911, Bác đã trả lời một nhà báo Nga như sau: “Khi tôi độ mười ba tuổi, lần đầu tiên tôi được nghe ba chữ Pháp Tự do, Bình đẳng, Bác ái... Tôi rất muốn làm quen với nền văn minh Pháp, muốn tìm xem những gì ẩn giấu đằng sau những chữ ấy”. Trả lời một nhà văn Mỹ cũng về câu hỏi này, Người nói: “Nhân dân Việt Nam trong đó có ông cụ thân sinh ra tôi, lúc này thường tự hỏi nhau ai sẽ là người giúp mình thoát khỏi ách thống trị của Pháp. Người này nghĩ là Anh, có người lại cho là Mỹ. Tôi thấy phải đi ra nước ngoài xem cho rõ. Sau khi xem xét họ làm ăn ra sao, tôi sẽ trở về giúp đồng bào tôi”.
- Năm 1953, để cung cấp tài liệu học tập cho cán bộ, đảng viên, Chủ tịch Hồ Chí Minh viết 50 bài báo giới thiệu có hệ thống những kiến thức chính trị phổ thông, những đạo lý cách mạng cơ bản, đăng trên nhiều số báo của Báo Cứu quốc với bút danh Đ.X. Loạt bài sau này được xuất bản thành sách với tiêu đề “Thường thức chính trị”. Trong loạt bài đã đăng, bài “Chính sách kinh tế của Đảng và Chính phủ” đăng ngày 5-6-1953.
- Ngày 5-6-1968, Bác gửi thư khen cán bộ, chiến sĩ đảo Cồn Cỏ do có thành tích chiến đấu dũng cảm, bắn rơi 4 máy bay Mỹ trong ngày 31-5-1968. Bác nhắc cán bộ, chiến sĩ đảo phải tăng cường đoàn kết, luôn nâng cao cảnh giác, không ngừng tập luyện, sẵn sàng chiến đấu, kiên quyết đập tan mọi âm mưu, thủ đoạn của địch, giành nhiều thắng lợi to lớn hơn nữ cuối thư Bác gửi tặng 2 câu thơ:
“Cồn Cỏ nở đầy hoa thắng trận,
Đánh cho tan xác giặc Hoa Kỳ”.
(Sách Chủ tịch Hồ Chí Minh ngày này năm xưa, NXB Chính trị Quốc gia - Sự thật, 2010 và Hồ Chí Minh toàn tập, NXB Chính trị Quốc gia - Sự thật, 2011).
Bác Hồ ra đi tìm đường cứu nước ở đâu?
Tính quyền lực về tổ chức và hoạt động của bộ máy nhà nước Cộng hoà xã hội chủ nghĩa Việt Nam thể hiện qua nội dung nào sau đây?
Tam thức bậc hai \(f(x) = {x^2} + (\sqrt 5 - 1)x - \sqrt 5 \) nhận giá trị dương khi?
Cá nhân, hộ gia đình, doanh nghiệp,... trực tiếp tạo ra sản phẩm đáp ứng nhu cầu tiêu dùng của xã hội nhằm thu lợi nhuận được gọi là gì?
Read the following passage about home schooling in the UK and mark the letter A, B, C or D on your answer sheet to indicate the best answer to each of the following questions from 23 to 30.
Full-time education in the UK is compulsory from the age of five to sixteen, but this doesn’t have to be in a school. Around 50,000 children are educated at home. This is called ‘homeschooling’.
Parents take their children out of school for different reasons, like illness and the need for special care, or because the distance to the nearest school may be too far. Some children are simply unhappy at school. Whatever the reason, they’re allowed to study at home, although inspectors regularly check how they are getting on.
Hayley and Jenny haven’t been to school for two years but they haven’t neglected their studies. Their mother worked out strict timetables for them, with hourly lessons for each day. She’s responsible for teaching them Maths, English, History and French. Their father teaches them Science and Geography. They study all the other school subjects online. ‘We have lessons with Dad in the evenings and at weekends,’ explains Hayley.
The family’s home is in a remote part of Wales. ‘The girls were fine at school but they spent so much time getting to school, they were too tired to learn, says their mother, Julia”. ‘We had a family conference and in the end we decided to try homeschooling. So far, it’s been a big success, but the girls know that if they want to go back to school at any time, we’ll let them. We follow the normal school program of lessons, and they will take all the normal school exams.’
There are disadvantages too, of course. ‘Social isolation is something I worry about,’ says Julia. They both seem happy and well-adjusted, but they haven’t really got friends who live locally. But in the summer holidays they go away on trips to summer camps, where they have no trouble mixing with people and making friends.’
The word “well-adjusted” in paragraph 5 most probably means ______.
Loại thuốc thử nào được dùng để nhận biết sự có mặt của tinh bột trong tế bào?
Vì sao thực dân Pháp chú trọng xây dựng hệ thống giao thông trong cuộc khai thác thuộc địa lần thứ nhất?
Read the following passage about fitness trends and mark the letter A, B, C or D on your answer sheet to indicate the best answer to each of the following questions from 31 to 40.
FITNESS TRENDS
[I] Reformer Pilates is an advanced and more intense variation of traditional Pilates. [II] Since this type of equipment isn’t something you would typically have at home, you’ll need to visit a specialized Pilates center to try it. [III] While it might look easy at first, don’t be fooled - by the end of the session, your thighs will be burning, and you might struggle to walk up or down stairs for a few days afterward. [IV] This workout pushes your body to its limits, providing a more challenging experience than standard Pilates, and many find it an effective way to build both strength and flexibility.
Trampolining is another popular fitness trend, and although it may seem like child's play, it’s actually a highly effective workout. Jumping up and down on a trampoline can leave you feeling exhausted after just a few minutes. Surprisingly, it’s even better for heart health than running, while also improving coordination and helping to reduce stress levels. Trampolining is gaining widespread popularity, with new centers popping up that feature as many as 150 trampolines. These facilities offer options for everyone: you can enjoy 'freejumping, where you bounce without an instructor, or pay for professional lessons to learn the best techniques and get the most out of your workout. Many people are discovering that trampolining combines fun and fitness in a way that makes staying active much more enjoyable.
If you're someone who is typically active but feeling down or emotionally drained, Dynamic Running Therapy might be just what the doctor ordered. This trend involves running with a therapist, combining the benefits of physical exercise with talk therapy. Though these sessions are often more expensive than typical therapy sessions because of the professional fees, they offer significant advantages. Running while talking helps distract you from any discomfort, allowing you to cover longer distances, and creates a relaxed, open environment that can make it easier to talk compared to the usual therapist’s office setting.
Which of the following is TRUE according to the passage?
Quyền và nghĩa vụ trong việc thực hiện pháp luật về ngân sách nhà nước được thể hiện qua các nội dung nào dưới đây?
Cho tứ diện ABCD. Lấy điểm I bất kì thuộc cạnh AC. Qua I kẻ đường thẳng song song với AB cắt BC tại M. Qua I kẻ đường thẳng song song với CD cắt AD tại N. Khi đó, góc giữa hai đường thẳng AB và CD là?
Có bao nhiêu loại kế hoạch tài chính của cá nhân?
Read the following passage about Generations Z and Alpha: Born Multicultural Citizens and mark the letter A, B, C or D on your answer sheet to indicate the option that best fits each of the numbered blanks from 18 to 22.
Generation Z, born between 1997 and 2012, has grown up in a world (18)_________. These young people use smartphones and computers every day to talk with friends from different parts of the world. If they had been born 30 years earlier, they would not have had these opportunities to experience global connections. They are learning about different cultures, languages, and traditions not just from books but through real online friendships.
Generation Alpha, which includes children born after 2013, is even more connected. The toys that Generation Alpha plays with often teach them about global issues while they have fun. Many schools (19)_________. These young students, who come from diverse backgrounds, are creating a new kind of society where differences are celebrated.
(20)_________. Generation Z students participate in exchange programs and travel more than previous generations did. (21)_________, sharing their daily lives and learning from each other.
The world that these generations are creating will be more inclusive and understanding. Traditional borders are becoming less important while cultural exchange is valued more highly. Generation Z and Alpha children, (22)_________, will likely become adults who solve problems together across cultural lines. The future looks promising with these multicultural citizens leading the way.
Phủ định của mệnh đề "n>9" là
