Question

Rút gọn các biểu thức

\(x^2+\sqrt{x^4-8x^2+16}\)

Answer 1

\(x^2+\sqrt{x^4-8x^2+16}=x^2+\sqrt{\left(x^2-4\right)^2}=x^2+\left|x^2-4\right|\)

Answer 2

\(x^2+\sqrt{x^4-8x^2+16}=x^2+\sqrt{\left(x^2-4\right)^2}=x^2+\left|x^2-4\right|\) `(1)`

`@`TH1: \(x^2-4\ge0\Rightarrow x\ge2\)

\(\left(1\right)\Rightarrow x^2+x^2-4=2x^2-4\)

`@`TH2:\(x^2-4< 0\Rightarrow x< 2\)

\(\left(1\right)\Rightarrow x^2+4-x^2=4\)