Question

Rút gọc biểu thức

Answer 1

c) \(\sqrt{\left(x-2\right)^2}+\dfrac{x-2}{\sqrt{\left(x-2\right)^2}}\)

\(=\left|x-2\right|+\dfrac{x-2}{\left|x-2\right|}\)

TH1: \(\left|x-2\right|=-\left(x-2\right)\) với \(x< 2\) 

\(\Rightarrow-\left(x-2\right)+\dfrac{x-2}{-\left(x-2\right)}=-x+2-1=-x+1\)

TH2: \(\left|x-2\right|=x-2\) với \(x\ge2\)

\(\Rightarrow x-2+\dfrac{x-2}{x-2}=x-2+1=x-1\)

d) \(\sqrt{a}-\sqrt{a-2\sqrt{a}+1}\)

\(=\sqrt{a}-\sqrt{\left(\sqrt{a}\right)^2-2\cdot\sqrt{a}\cdot1-1^2}\)

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

\(=\sqrt{a}-\left|\sqrt{a}-1\right|\)

TH1: \(\left|\sqrt{a}-1\right|=-\left(\sqrt{a}-1\right)\) với \(a< 1\)

\(\Rightarrow\sqrt{a}-\left[-\left(\sqrt{a}-1\right)\right]=\sqrt{a}+\sqrt{a}-1=2\sqrt{a}-1\)

TH2: \(\left|\sqrt{a}-1\right|=\sqrt{a}-1\) với \(a\ge1\)

\(\Rightarrow\sqrt{a}-\left(\sqrt{a}-1\right)=\sqrt{a}-\sqrt{a}+1=1\)

Answer 2

\(ww\dfrac{w}{w}\)

Answer 3

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