Question

[Ut02_huong]

Cho 4 số a, b, x, y sao cho ab=1; ax+by=1. CMR xy\(\le\)1

Answer 1

[Nguyễn Nhật Minh]

\(\left(ax+by\right)^2=1\Leftrightarrow\left(ax\right)^2+2abxy+\left(by\right)^2=1\Leftrightarrow2xy\le1\Leftrightarrow xy\le\frac{1}{2}\)