Question

tìm GTLN của biểu thức sau :M =\(\frac{6}{X-2\sqrt{X}+3}\)

Answer 1

Ta có \(X-2\sqrt{X}+3\)

\(=\sqrt{X}^2+2\times\sqrt{X}\times1+1^2+2\)

\(=\left(\sqrt{X}+1\right)^2+2\)

Ta lại có \(\left(\sqrt{X}+1\right)^2\ge0,\forall X\)

\(\Rightarrow P\le3.\)Dấu"=" xảy ra khi \(\sqrt{X}+1=0\)\(\Leftrightarrow X=1\)

Vậy MaxP=3<=>X=1

Answer 2

Ta có X-2\sqrt{X}+3X−2X​+3

=\sqrt{X}^2+2\times\sqrt{X}\times1+1^2+2=X​2+2×X​×1+12+2

=\left(\sqrt{X}+1\right)^2+2=(X​+1)2+2

Ta lại có \left(\sqrt{X}+1\right)^2\ge0,\forall X(X​+1)2≥0,∀X

\Rightarrow P\le3.⇒P≤3.Dấu"=" xảy ra khi \sqrt{X}+1=0X​+1=0\Leftrightarrow X=1⇔X=1

Vậy Max P=3<=>X=1