Toán Cho a+b+c=3, a,b,c>0. Tìm min a^2020+b^2020+c^2020 05/08/2021 By Ayla Cho a+b+c=3, a,b,c>0. Tìm min a^2020+b^2020+c^2020
Ta có: ` a^{2020} ≥ 0 ; b^{2020} ≥ 0 ; c^{2020} ≥ 0 ` ` => a^{2020} + b^{2020} + c^{2020} ≥ 0 ` Do: ` a + b + c = 3 ; a , b , c > 0 ` ` => a^{2020} + b^{2020} + c^{2020} ≥ 3 ` Vậy ` M i n_{a^{2020} + b^{2020} + c^{2020}} ` là ` 3, ` Dấu ` “=” ` xảy ra khi: ` a = b = c = 1 ` Trả lời
Ta có:
` a^{2020} ≥ 0 ; b^{2020} ≥ 0 ; c^{2020} ≥ 0 `
` => a^{2020} + b^{2020} + c^{2020} ≥ 0 `
Do: ` a + b + c = 3 ; a , b , c > 0 `
` => a^{2020} + b^{2020} + c^{2020} ≥ 3 `
Vậy ` M i n_{a^{2020} + b^{2020} + c^{2020}} ` là ` 3, ` Dấu ` “=” ` xảy ra khi: ` a = b = c = 1 `