Question

cho \(\sqrt{x}+2\sqrt{y}=10\)chứng minh rằng \(x+y\ge20\)

Answer 1

Áp dụng BĐT Cauchy–Schwarz ta có:

\(\left(1^2+2^2\right)\left(x+y\right)\ge\left(\sqrt{x}+2\sqrt{y}\right)^2\)

<=>   \(5\left(x+y\right)\ge100\)

<=>  \(x+y\ge20\)

Dấu "=" xảy ra  <=>  \(x=4;\)\(y=16\)

Answer 2

ban duong quynh giang oi bdt ay phai la bunhiacopxki moi dung