Question

Tìm giá trị nhỏ nhất của \(a-2\sqrt{ab}+3b-2\sqrt{a}+1\)

Answer 1

\(3b+a-2\sqrt{ab}-2\sqrt{a}+1\)

\(=\left(3b-\frac{2.\sqrt{3ab}}{\sqrt{3}}+\frac{a}{3}\right)+\left(\frac{2a}{3}-\frac{2.\sqrt{a}.\sqrt{2}.\sqrt{3}}{\sqrt{3}.\sqrt{2}}+\frac{3}{2}\right)-\frac{1}{2}\)

\(=\left(\sqrt{3b}-\frac{\sqrt{a}}{\sqrt{3}}\right)^2+\left(\sqrt{\frac{2a}{3}}-\sqrt{\frac{3}{2}}\right)^2-\frac{1}{2}\ge-\frac{1}{2}\)

Dấu = xảy ra khi \(\hept{\begin{cases}a=\frac{9}{4}\\b=\frac{1}{4}\end{cases}}\)

Answer 2

I don't know because I don't understand!

Answer 3

I DON'T KNOW DON'T CARE!

:v