Question

If , $x=2-\sqrt{3}$, then the value of $x^2–4x+8$ is equal to

• A. 7
• B. 4
• C. 3
• D. 0

Answer 1

The correct option is A 7

$x=2-\sqrt{3}$
$\Rightarrow x-2=-\sqrt{3}$
$\Rightarrow (x-2{)}^2=(-\sqrt{3}{)}^2=3$
$\Rightarrow x^2–4x+4=3$ [$\because (a–b{)}^2=a^2–2ab+b^2$]
$\Rightarrow x^2–4x=–1$
$\Rightarrow x^2–4x+8=–1+8=7$
Thus, the value of $x^2–4x+8$ is 7.
Hence, the correct answer is option (1).