Question

Tìm x để \(A=\dfrac{4x-5}{\sqrt{4x-3}-\sqrt{2}}\) đạt GTNN.

@Ace Legona

Answer 1

ĐK: \(x\ge\dfrac{3}{4}\)

ta có

\(\sqrt{4x-3}-\sqrt{2}=\dfrac{4x-3-2}{\sqrt{4x-3}+\sqrt{2}}=\dfrac{4x-5}{\sqrt{4x-3}+\sqrt{2}}\)

\(\Rightarrow\dfrac{4x-5}{\sqrt{4x-3}-\sqrt{2}}=\dfrac{4x-5}{\dfrac{4x-5}{\sqrt{4x-3}+\sqrt{2}}}=\sqrt{4x-3}+\sqrt{2}\ge0+\sqrt{2}=\sqrt{2}\)

Đẳng thức xảy ra \(\Leftrightarrow\sqrt{4x-3}=0\Leftrightarrow x=\dfrac{3}{4}\)

Answer 2

Phương An gấp =(((