Question

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

Answer 1

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

Answer 2

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

`@` Với \(x\ge2\) và \(x\le-2\) \(\Rightarrow x^2+x^2-4=2x^2-4\)

`@` Với\(-2< x< 2\) \(\Rightarrow x^2+4-x^2=4\)

Answer 3

x2+ \(\sqrt{x^4-8x^2}+16\) = x² + \(\sqrt{\left(x^2-4\right)^2}\) = x² + \(\left|x^2-4\right|\) = x² + x²  - 4 = 2x² - 4