Question

[Known]

Cho a;b khác 0

Tìm GTLN: \(A=\frac{7\left(a+b\right)^2-9\left(a-b\right)^2}{2014\left(a^2+b^2\right)}\)

Answer 1

[Girl]

\(7\left(a+b\right)^2-9\left(a-b\right)^2=7\left(a^2+2ab+b^2\right)-9\left(a^2-2ab+b^2\right)\)

\(=-2a^2-2b^2+32ab\)

Từ bđt \(2ab\le a^2+b^2\Rightarrow\)\(32ab\le16\left(a^2+b^2\right)\Rightarrow-2a^2-2b^2+32ab\le14\left(a^2+b^2\right)\)

\(\Rightarrow A\le\frac{14\left(a^2+b^2\right)}{2014\left(a^2+b^2\right)}=\frac{7}{1007}\)

\("="\Leftrightarrow a=b\)

Answer 2

[cao van duc]

bn ơi a,b khác 0 chứ chưa dương bn sao  dùng đc cô si