Question

A=\(\left(\dfrac{\sqrt{a}}{2}-\dfrac{1}{2\sqrt{a}}\right)^2\left(\dfrac{\sqrt{a}-1}{\sqrt{a}+1}-\dfrac{\sqrt{a}+1}{\sqrt{a}-1}\right)\)

a)rút gọn

b)tìm a để A<0

c)tìm a để A=-2

Answer 1

a: \(A=\left(\dfrac{a-1}{2\sqrt{a}}\right)^2\cdot\dfrac{a-2\sqrt{a}+1-a-2\sqrt{a}-1}{a-1}\)

\(=\dfrac{\left(a-1\right)^2}{4a}\cdot\dfrac{-4\sqrt{a}}{a-1}=\dfrac{-\left(a-1\right)}{\sqrt{a}}\)

b: Để A<0 thì -(a-1)<0

=>a-1>0

=>a>1

c: Để A=-2 thì \(-\left(a-1\right)=-2\sqrt{a}\)

=>a-1-2 căn a=0

=>căn a=1+căn 2

hay \(a=3+2\sqrt{2}\)