Question

Cho \(A=\dfrac{2\sqrt{a}-9}{a-5\sqrt{a}+6}-\dfrac{\sqrt{a}+3}{\sqrt{a}+2}-\dfrac{2\sqrt{a}+1}{3-\sqrt{a}}\)

a) Rút gọn A.

b) Tính A khi \(a=3+2\sqrt{2}\)

c) Tìm a để A < 1

d) Tìm a ⊂ Z để A ⊂ Z

Answer 1

a: \(A=\dfrac{2\sqrt{a}-9-a+9+2a-4\sqrt{a}+\sqrt{a}-2}{\left(\sqrt{a}-2\right)\left(\sqrt{a}-3\right)}\)

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

b: Khi a=3+2 căn 2 thì 

\(A=\dfrac{\sqrt{2}+1+1}{\sqrt{2}+1-3}=\dfrac{2+\sqrt{2}}{\sqrt{2}-2}=\dfrac{\sqrt{2}+1}{1-\sqrt{2}}=-3-2\sqrt{2}\)

c: Để A<1 thì A-1<0

=>căn a+1-căn a+3/căn a-3<0

=>căn a-3<0

=>0<=a<9