Question

If $f\left(x\right)=x^2-2\sqrt{2}x+1,\mathrm{then}f\left(2\sqrt{2}\right)$ is equal to
(a) 0
(b) 1
(c) $4\sqrt{2}$
(d) $8\sqrt{2}+1$

Answer 1

Given: f(x) = $x^2-2\sqrt{2}x+1$

$$\begin{gathered} f\left(2\sqrt{2}\right)={\left(2\sqrt{2}\right)}^2-2\sqrt{2}\left(2\sqrt{2}\right)+1 \\ ={\left(2\sqrt{2}\right)}^2-{\left(2\sqrt{2}\right)}^2+1 \\ =1 \end{gathered}$$
​
Hence, the correct option is (b).