Cho a,b , c  là các số thực thuộc đoạn \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaaca % aIXaGaai4oaiaaikdaaiaawUfacaGLDbaaaaa!3A1C! \left[ {1;2} \right]\) thỏa mãn \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciiBaiaac+ % gacaGGNbWaa0baaSqaaiaaikdaaeaacaaIZaaaaOGaamyyaiabgUca % RiGacYgacaGGVbGaai4zamaaDaaaleaacaaIYaaabaGaaG4maaaaki % aadkgacqGHRaWkciGGSbGaai4BaiaacEgadaqhaaWcbaGaaGOmaaqa % aiaaiodaaaGccaWGJbGaeyizImQaaGymaiaac6caaaa!4B0F! \log _2^3a + \log _2^3b + \log _2^3c \le 1.\) Khi biểu thức \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiuaiabg2 % da9iaadggadaahaaWcbeqaaiaaiodaaaGccqGHRaWkcaWGIbWaaWba % aSqabeaacaaIZaaaaOGaey4kaSIaam4yamaaCaaaleqabaGaaG4maa % aakiabgkHiTiaaiodadaqadaqaaiGacYgacaGGVbGaai4zamaaBaaa % leaacaaIYaaabeaakiaadggadaahaaWcbeqaaiaadggaaaGccqGHRa % WkciGGSbGaai4BaiaacEgadaWgaaWcbaGaaGOmaaqabaGccaWGIbWa % aWbaaSqabeaacaWGIbaaaOGaey4kaSIaciiBaiaac+gacaGGNbWaaS % baaSqaaiaaikdaaeqaaOGaam4yamaaCaaaleqabaGaam4yaaaaaOGa % ayjkaiaawMcaaaaa!5570! P = {a^3} + {b^3} + {c^3} - 3\left( {{{\log }_2}{a^a} + {{\log }_2}{b^b} + {{\log }_2}{c^c}} \right)\) đạt giá trị lớn nhất thì giá trị của tổng a + b + c là 

Đặt \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEaiabg2 % da9iGacYgacaGGVbGaai4zamaaBaaaleaacaaIYaaabeaakiaadgga % caGG7aGaamyEaiabg2da9iGacYgacaGGVbGaai4zamaaBaaaleaaca % aIYaaabeaakiaadkgacaGG7aGaamOEaiabg2da9iGacYgacaGGVbGa % ai4zamaaBaaaleaacaaIYaaabeaakiaadogacaGGUaaaaa!4C2B! x = {\log _2}a;y = {\log _2}b;z = {\log _2}c.\) Vì \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyyaiaacY % cacaWGIbGaaiilaiaadogacqGHiiIZdaWadaqaaiaaigdacaGG7aGa % aGPaVlaaikdaaiaawUfacaGLDbaaaaa!4140! a,b,c \in \left[ {1;\,2} \right]\) nên \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEaiaacY % cacaaMc8UaaGPaVlaadMhacaGGSaGaaGPaVlaaykW7caWG6bGaeyic % I48aamWaaeaacaaIWaGaai4oaiaaigdaaiaawUfacaGLDbaaaaa!4624! x,\,\,y,\,\,z \in \left[ {0;1} \right]\)

\(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaWGqb % Gaeyypa0JaamyyamaaCaaaleqabaGaaG4maaaakiabgUcaRiaadkga % daahaaWcbeqaaiaaiodaaaGccqGHRaWkcaWGJbWaaWbaaSqabeaaca % aIZaaaaOGaeyOeI0IaaG4mamaabmaabaGaciiBaiaac+gacaGGNbWa % aSbaaSqaaiaaikdaaeqaaOGaamyyamaaCaaaleqabaGaamyyaaaaki % abgUcaRiGacYgacaGGVbGaai4zamaaBaaaleaacaaIYaaabeaakiaa % dkgadaahaaWcbeqaaiaadkgaaaGccqGHRaWkciGGSbGaai4BaiaacE % gadaWgaaWcbaGaaGOmaaqabaGccaWGJbWaaWbaaSqabeaacaWGJbaa % aaGccaGLOaGaayzkaaaabaGaaGPaVlaaykW7caaMc8UaaGPaVlaayk % W7cqGH9aqpcaWGHbWaaWbaaSqabeaacaaIZaaaaOGaey4kaSIaamOy % amaaCaaaleqabaGaaG4maaaakiabgUcaRiaadogadaahaaWcbeqaai % aaiodaaaGccqGHsislcaaIZaWaaeWaaeaacaWGHbGaciiBaiaac+ga % caGGNbWaaSbaaSqaaiaaikdaaeqaaOGaamyyaiabgUcaRiaadkgaci % GGSbGaai4BaiaacEgadaWgaaWcbaGaaGOmaaqabaGccaWGIbGaey4k % aSIaam4yaiGacYgacaGGVbGaai4zamaaBaaaleaacaaIYaaabeaaki % aadogaaiaawIcacaGLPaaaaeaacaaMc8UaaGPaVlaaykW7caaMc8Ua % aGPaVlabg2da9iaadggadaahaaWcbeqaaiaaiodaaaGccqGHRaWkca % WGIbWaaWbaaSqabeaacaaIZaaaaOGaey4kaSIaam4yamaaCaaaleqa % baGaaG4maaaakiabgkHiTiaaiodadaqadaqaaiaadggacaWG4bGaey % 4kaSIaamOyaiaadMhacqGHRaWkcaWGJbGaamOEaaGaayjkaiaawMca % aiaac6caaaaa!969B! \begin{array}{l} P = {a^3} + {b^3} + {c^3} - 3\left( {{{\log }_2}{a^a} + {{\log }_2}{b^b} + {{\log }_2}{c^c}} \right)\\ \,\,\,\,\, = {a^3} + {b^3} + {c^3} - 3\left( {a{{\log }_2}a + b{{\log }_2}b + c{{\log }_2}c} \right)\\ \,\,\,\,\, = {a^3} + {b^3} + {c^3} - 3\left( {ax + by + cz} \right). \end{array}\)

Ta chứng minh \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyyamaaCa % aaleqabaGaaG4maaaakiabgkHiTiaaiodacaWGHbGaamiEaiabgsMi % JkaadIhadaahaaWcbeqaaiaaiodaaaGccqGHRaWkcaaIXaGaaiOlaa % aa!4150! {a^3} - 3ax \le {x^3} + 1.\) Thật vậy

Xét hàm số :\(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzamaabm % aabaGaamyyaaGaayjkaiaawMcaaiabg2da9iaadggacqGHsislciGG % SbGaai4BaiaacEgadaWgaaWcbaGaaGOmaaqabaGccaWGHbGaaiilai % aaykW7caWGHbGaeyicI48aamWaaeaacaaIXaGaai4oaiaaykW7caaM % c8UaaGOmaaGaay5waiaaw2faaiabgkDiElqadAgagaqbamaabmaaba % GaamyyaaGaayjkaiaawMcaaiabg2da9iaaigdacqGHsisldaWcaaqa % aiaaigdaaeaacaWGHbGaciiBaiaac6gacaaIYaaaaiabgkDiElqadA % gagaqbamaabmaabaGaamyyaaGaayjkaiaawMcaaiabg2da9iaaicda % cqGHuhY2caWGHbGaeyypa0ZaaSaaaeaacaaIXaaabaGaciiBaiaac6 % gacaaIYaaaaaaa!68AA! f\left( a \right) = a - {\log _2}a,\,a \in \left[ {1;\,\,2} \right] \Rightarrow f'\left( a \right) = 1 - \frac{1}{{a\ln 2}} \Rightarrow f'\left( a \right) = 0 \Leftrightarrow a = \frac{1}{{\ln 2}}\)

Trên đoạn \([1;2]\) ta có \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzamaabm % aabaGaamyyaaGaayjkaiaawMcaaiabgsMiJkaab2eacaqGHbGaaeiE % amaacmaabaGaamOzamaabmaabaGaaGymaaGaayjkaiaawMcaaiaacY % cacaWGMbWaaeWaaeaacaaIYaaacaGLOaGaayzkaaGaaiilaiaadAga % daqadaqaamaalaaabaGaaGymaaqaaiGacYgacaGGUbGaaGOmaaaaai % aawIcacaGLPaaaaiaawUhacaGL9baacqGH9aqpcaaIXaGaeyO0H4Ta % amyyaiabgkHiTiGacYgacaGGVbGaai4zamaaBaaaleaacaaIYaaabe % aakiaadggacqGHKjYOcaaIXaaaaa!5A8A! f\left( a \right) \le {\rm{Max}}\left\{ {f\left( 1 \right),f\left( 2 \right),f\left( {\frac{1}{{\ln 2}}} \right)} \right\} = 1 \Rightarrow a - {\log _2}a \le 1\)

hay \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyyaiabgk % HiTiaadIhacqGHKjYOcaaIXaGaeyi1HSTaamyyaiabgkHiTiaadIha % cqGHsislcaaIXaGaeyizImQaaGimaiaac6caaaa!4529! a - x \le 1 \Leftrightarrow a - x - 1 \le 0.\) Do đó.

Xét: \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyyamaaCa % aaleqabaGaaG4maaaakiabgkHiTiaaiodacaWGHbGaamiEaiabgkHi % TiaadIhadaahaaWcbeqaaiaaiodaaaGccqGHsislcaaIXaGaeyypa0 % ZaaeWaaeaacaWGHbGaeyOeI0IaamiEaiabgkHiTiaaigdaaiaawIca % caGLPaaadaqadaqaaiaadggadaahaaWcbeqaaiaaikdaaaGccqGHRa % WkcaWG4bWaaWbaaSqabeaacaaIYaaaaOGaey4kaSIaaGymaiabgUca % RiaadggacqGHRaWkcaWGHbGaamiEaiabgkHiTiaadIhaaiaawIcaca % GLPaaacqGHKjYOcaaIWaaaaa!579E! {a^3} - 3ax - {x^3} - 1 = \left( {a - x - 1} \right)\left( {{a^2} + {x^2} + 1 + a + ax - x} \right) \le 0\)

Vậy \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyyamaaCa % aaleqabaGaaG4maaaakiabgkHiTiaaiodacaWGHbGaamiEaiabgkHi % TiaadIhadaahaaWcbeqaaiaaiodaaaGccqGHsislcaaIXaGaeyizIm % QaaGimaaaa!4250! {a^3} - 3ax - {x^3} - 1 \le 0\) \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyi1HSTaam % yyamaaCaaaleqabaGaaG4maaaakiabgkHiTiaaiodacaWGHbGaamiE % aiabgsMiJkaadIhadaahaaWcbeqaaiaaiodaaaGccqGHRaWkcaaIXa % aaaa!42FA! \Leftrightarrow {a^3} - 3ax \le {x^3} + 1\)Tương tự \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyi1HSTaam % yyamaaCaaaleqabaGaaG4maaaakiabgkHiTiaaiodacaWGHbGaamiE % aiabgsMiJkaadIhadaahaaWcbeqaaiaaiodaaaGccqGHRaWkcaaIXa % aaaa!42FA! \Leftrightarrow {a^3} - 3ax \le {x^3} + 1\); \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4yamaaCa % aaleqabaGaaG4maaaakiabgkHiTiaaiodacaWGJbGaamOEaiabgsMi % JkaadQhadaahaaWcbeqaaiaaiodaaaGccqGHRaWkcaaIXaaaaa!40A6! {c^3} - 3cz \le {z^3} + 1\)

Do đó :\(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiuaiaayk % W7cqGH9aqpcaWGHbWaaWbaaSqabeaacaaIZaaaaOGaey4kaSIaamOy % amaaCaaaleqabaGaaG4maaaakiabgUcaRiaadogadaahaaWcbeqaai % aaiodaaaGccqGHsislcaaIZaWaaeWaaeaacaWGHbGaamiEaiabgUca % RiaadkgacaWG5bGaey4kaSIaam4yaiaadQhaaiaawIcacaGLPaaaca % aMc8UaeyizImQaamiEamaaCaaaleqabaGaaG4maaaakiabgUcaRiaa % dMhadaahaaWcbeqaaiaaiodaaaGccqGHRaWkcaWG6bWaaWbaaSqabe % aacaaIZaaaaOGaey4kaSIaaG4maiabgsMiJkaaigdacqGHRaWkcaaI % ZaGaeyypa0JaaGinaaaa!5DA1! P\, = {a^3} + {b^3} + {c^3} - 3\left( {ax + by + cz} \right)\, \le {x^3} + {y^3} + {z^3} + 3 \le 1 + 3 = 4\)

Đẳng thức xảy ra khi và chỉ khi \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEaiabg2 % da9iaadMhacqGH9aqpcaaIWaGaaiilaiaadQhacqGH9aqpcaaIXaaa % aa!3E25! x = y = 0,z = 1\) và các hoán vị, tức là \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyyaiabg2 % da9iaadkgacqGH9aqpcaaIXaGaaiilaiaadogacqGH9aqpcaaIYaaa % aa!3DE2! a = b = 1,c = 2\) và các hoán vị. Khi đó \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyyaiabgU % caRiaadkgacqGHRaWkcaWGJbGaeyypa0JaaGinaaaa!3C31! a + b + c = 4\)