Question

1) rút gọn biểu thức :

a) \(\sqrt{\left(2-\sqrt{5}\right)^2}\)

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

c) \(\sqrt{\left(a-3\right)^2}+\left(a-9\right)\) (với a<3)

d) \(\sqrt{\left(2a+5\right)^2}-\left(2a-7\right)\)

Answer 1

a, \(\sqrt{\left(2-\sqrt{5}\right)^2}=\sqrt{5}-2\left(\sqrt{5}>2\right)\)

b, \(\sqrt{\left(3-\sqrt{2}\right)^2}=3-\sqrt{2}\left(3>\sqrt{2}\right)\)

c, Với a < 3

\(\sqrt{\left(a-3\right)^2}+\left(a-9\right)=3-a+a-9=-6\)

d, \(A=\sqrt{\left(2a+5\right)^2}-\left(2a-7\right)\)

\(=\left|2a+5\right|-2a+7\)

+) Xét \(x\ge\dfrac{-5}{2}\) có:

\(A=2a+5-2a+7=12\)

+) Xét \(x< \dfrac{-5}{2}\) có:
\(A=-2a-5-2a+7=-4a+2\)

Vậy...

Answer 2

\(a,A=\sqrt{5}-2\\ b,B=3-\sqrt{2}\\ c,C=3-a+a-9\\ =-6\\ d,D=2a+5-2a+7\\ =12\)