Question

Tính

a) \(\sqrt{12}+\dfrac{4}{\sqrt{3}-\sqrt{5}}\)

b) \(\sqrt{\left(1+\sqrt{2}\right)^2}\)+ \(\sqrt{\left(\sqrt{2}-3\right)^2}\)

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

a) Tìm ĐKXĐ

b) Rút gọn

c) Tính P khi x = \(\dfrac{1}{4}\)

Tìm x để P < 1

Answer 1

Bài 2:

a: ĐKXĐ: x>0; x<>1

b: \(P=\dfrac{\sqrt{x}+1+\sqrt{x}-1}{x-1}\cdot\dfrac{\sqrt{x}-1}{\sqrt{x}}=\dfrac{2}{\sqrt{x}+1}\)

c: Khi x=1/4 thì \(P=2:\left(\dfrac{1}{2}+1\right)=2:\dfrac{3}{2}=\dfrac{4}{3}\)