Question

Cho P = \(\dfrac{x-3\sqrt{x}+2}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\). CM: P < \(\dfrac{1}{3}\)

Answer 1

P = \(\dfrac{x-\sqrt{x}-2\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\)

P=\(\dfrac{\left(\sqrt{x}-1\right)\left(\sqrt{x}-2\right)}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\)

P=\(\dfrac{\sqrt{x}+2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)+\sqrt{x}+2}\)

3P=\(\dfrac{3\sqrt{x}+6}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)+\sqrt{x}+2}\)

vì 2(\(\sqrt{x}+2\))>\(\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)\)=>3p>1=>P>\(\dfrac{1}{3}\)