Question

Áp dụng bất đẳng thức cô-si tìm max

a) A=-x^2+2x+7

b) B=(x-y)(5-2x+2y)+14

Giúp mình nha!!!!

Answer 1

a: =-(x^2-2x-7)

=-(x^2-2x+1-8)

=-(x-1)^2+8<=8

Dấu = xảy ra khi x=1

b: \(B=\left(x-y\right)\left[-2\left(x-y\right)+5\right]+14\)

\(=-2\left(x-y\right)^2+5\left(x-y\right)+14\)

\(=-2\left[\left(x-y\right)^2-\dfrac{5}{2}\left(x-y\right)-7\right]\)

\(=-2\left[\left(x-y\right)^2-2\cdot\left(x-y\right)\cdot\dfrac{5}{4}+\dfrac{25}{16}-\dfrac{137}{16}\right]\)

\(=-2\left(x-y-\dfrac{5}{4}\right)^2+\dfrac{137}{8}< =\dfrac{137}{8}\)

Dấu = xảy ra khi x=y+5/4