Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
a, \(\sqrt{\left(\sqrt{2}\right)^2+2\times2\times\sqrt{2}+2^2}\)+ \(\sqrt{2^2+2\times2\times\sqrt{2}+\left(\sqrt{2}\right)^2}\)
= \(\sqrt{\left(\sqrt{2}+2\right)^2}\)+ \(\sqrt{\left(2-\sqrt{2}\right)^2}\)
= \(\sqrt{2}+2+2-\sqrt{2}\)
= 4
a)\(\sqrt{\frac{\left(x-2\right)^4}{\left(3-x\right)^2}}+\frac{x^2-1}{x-3}=\frac{\sqrt{\left(x-2\right)^4}}{\sqrt{\left(3-x\right)^2}}+\frac{x^2-1}{x-3}=\frac{\left(x-2\right)^2}{x-3}+\frac{x^2-1}{x-3}=\frac{x^2-4x+4+x^2-1}{x-3}=\frac{2x^2-4x+3}{x-3}\)
Tại x=0,5 thay vào ta có:
\(A=\frac{2\cdot\left(0,5\right)^2-4\cdot0,5+3}{0,5-3}=-\frac{3}{5}\)
b)\(4x-\sqrt{8}+\frac{\sqrt{x^3+2x^2}}{\sqrt{x+2}}=4x-\sqrt{8}+\frac{\sqrt{x^2\left(x+2\right)}}{\sqrt{x+2}}=4x-\sqrt{8}+\frac{\sqrt{x^2}\cdot\sqrt{x+2}}{\sqrt{x+2}}\)\(=4x-\sqrt{8}+x^2\)
Tại \(x=-\sqrt{2}\) thay vào ta có:
\(B=4\cdot\left(-\sqrt{2}\right)+\left(-\sqrt{2}\right)^2=2-4\sqrt{2}\)
a) \(x+3+\sqrt{x^2-6x+9}\left(x\le3\right)\)
\(=x+3+\sqrt{\left(x-3\right)^2}\)
\(=x+3+\left|x-3\right|\)
\(=x+3-\left(x-3\right)\)
\(=x+3-x+3\)
\(=6\)
b) \(\sqrt{x^2+4x+4}-\sqrt{x^2}\left(-2\le x\le0\right)\)
\(=\sqrt{\left(x+2\right)^2}-\sqrt{x^2}\)
\(=\left|x+2\right|-\left|x\right|\)
\(=x+2-\left(-x\right)\)
\(=x+2+x\)
\(=2x+2=2\left(x+1\right)\)
c) \(\frac{\sqrt{x^2-2x+1}}{x-1}\left(x>1\right)\)
\(=\frac{\sqrt{\left(x-1\right)^2}}{x-1}\)
\(=\frac{\left|x-1\right|}{x-1}\)
\(=\frac{x-1}{x-1}=1\)
d) \(\left|x-2\right|+\frac{\sqrt{x^2-4x+4}}{x-2}\)
\(=\left|x-2\right|+\frac{\sqrt{\left(x-2\right)^2}}{x-2}\)
\(=\left|x-2\right|+\frac{\left|x-2\right|}{x-2}\)
\(=\left|x-2\right|+\frac{-\left(x-2\right)}{x-2}\)
\(=\left|x-2\right|-1\)
\(=-\left(x-2\right)-1\)
\(=-x+2-1\)
\(=-x+1=-\left(x-1\right)\)
a: \(\sqrt{9\left(1+4x+4x^2\right)}=3\cdot\left|2x+1\right|\)
\(=3\left|-2\sqrt{3}+1\right|\)
\(=3\left(2\sqrt{3}-1\right)=6\sqrt{3}-3\)
b: \(\sqrt{4a^2\left(b^2+9-6b\right)}\)
\(=2\cdot\left|a\right|\cdot\left|b-3\right|\)
\(=2\cdot3\cdot\left|-\sqrt{2}-3\right|\)
\(=6\left(3+\sqrt{2}\right)\)