Question

Tìm Min của P biết:

P= x - 2\(\sqrt{2x-3}\)

Mik cần gấp mấy bạn ơi

Answer 1

\(P=x-2\sqrt{2x-3}\) (ĐK: \(x\ge\dfrac{3}{2}\) )

\(2P=2x-4\sqrt{2x-3}\)

\(2P=2x-3-4\sqrt{2x-3}+4-1\)

\(2P=\left(\sqrt{2x-3}-2\right)^2-1\) \(\ge-1\)

\(\Rightarrow P\ge\dfrac{-1}{2}\)

Dấu bằng xảy ra khi :

\(\sqrt{2x-3}=2\Leftrightarrow x=\dfrac{7}{2}\) (nhận)

Vậy .................

Answer 2

\(P=x-2\sqrt{2x-3}\) (ĐK: \(x\ge\dfrac{3}{2}\) )

\(2P=2x-4\sqrt{2x-3}\)

\(2P=2x-3-4\sqrt{2x-3}+4-1\)

\(2P=\left(\sqrt{2x-3}-2\right)^2-1\) \(\ge-1\)

\(\Rightarrow P\ge\dfrac{-1}{2}\)

Dấu bằng xảy ra khi :

\(\sqrt{2x-3}=2\Leftrightarrow x=\dfrac{7}{2}\) (nhận)

Vậy .................