Bất phương trình \({\log _2}\left( {2{x^4} + mx + m + 2025} \right) \ge {\log _2}\left( {2{x^4} + 2025} \right)\) nghiệm đúng với mọi \(x \in \mathbb{R}\) thì có bao nhiêu giá trị của tham số \(m\) thỏa mãn?
Bất phương trình \({\log _2}\left( {2{x^4} + mx + m + 2025} \right) \ge {\log _2}\left( {2{x^4} + 2025} \right)\) nghiệm đúng với mọi \(x \in \mathbb{R}\) thì có bao nhiêu giá trị của tham số \(m\) thỏa mãn?
Hãy suy nghĩ và trả lời câu hỏi trước khi xem đáp án
$2{x^4} + mx + m + 2025 \ge 2{x^4} + 2025$, $\forall x \in \mathbb{R}$
$\Leftrightarrow mx + m \ge 0$, $\forall x \in \mathbb{R}$
$\Leftrightarrow m(x+1) \ge 0$, $\forall x \in \mathbb{R}$
Để $m(x+1) \ge 0$ đúng với mọi $x \in \mathbb{R}$, thì $m = 0$.
Tuy nhiên, $m$ có thể nhận vô số giá trị âm, miễn là $x \ge -1$.
Xét $m = 0$ ta có $0 \ge 0$ (luôn đúng với mọi $x$).
Vì vậy có vô số giá trị $m$ thỏa mãn.
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Ø Show the features (4) ______ your customers that truly set you apart from the competition.
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Ø Join thousands of customers (3) ______ with their purchases and enjoy unparalleled performance.
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A few years ago, amid a record drought, scientists noticed something odd. A few of California’s giant sequoias inside Sequoia and Kings Canyon National Parks were dying in ways no one had ever documented – from the top down. When researchers climbed into the canopies, they discovered that beetles had bored into a few branches. By 2019, at least 38 of the trees had died – not a large number, but "concerning because we’ve never observed this before,” says Christy Brigham, the park’s chief of resource management.
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Phương án nào sau đây chỉ ra vai trò của kĩ thuật trong đời sống?
- Khi đặt hệ tọa độ
vào không gian với đơn vị trên trục tính theo kilômét, người ta thấy rằng một không gian phủ sóng điện thoại có dạng một hình cầu
. Biết mặt cầu
có phương trình
. Khoảng cách xa nhất giữa hai vùng phủ sóng là bao nhiêu kilômét?