Question

Q=(\(\dfrac{1}{\sqrt{a}-1}-\dfrac{1}{\sqrt{a}}\))(\(\dfrac{\sqrt{a}+1}{\sqrt{a}-2}-\dfrac{\sqrt{a}+2}{\sqrt{a}-1}\))
a, rút gọn

b, tìm x để Q>0

c, tính giá trị biểu thức khi a=9-4\(\sqrt{5}\)

Answer 1

a: \(Q=\dfrac{\sqrt{a}-\sqrt{a}+1}{\sqrt{a}\left(\sqrt{a}-1\right)}:\dfrac{a-1-a+4}{\left(\sqrt{a}-2\right)\left(\sqrt{a}-1\right)}\)

\(=\dfrac{1}{\sqrt{a}\left(\sqrt{a}-1\right)}\cdot\dfrac{\left(\sqrt{a}-2\right)\left(\sqrt{a}-1\right)}{3}\)

\(=\dfrac{\sqrt{a}-2}{3\sqrt{a}}\)

b: Để Q>0 thì căn a-2>0

=>a>4

c: Khi a=9-4 căn 5 thì \(Q=\dfrac{\sqrt{5}-2-2}{3\left(\sqrt{5}-2\right)}=\dfrac{-3-2\sqrt{5}}{3}\)