Question

If $x=\frac{2}{3+\sqrt{7}}$, then $(x-3{)}^2$=

• A. 1
• B. 3
• C. 6
• D. 7

Answer 1

The correct option is D

7

$x=\frac{2}{3+\sqrt{7}}=\frac{2(3-\sqrt{7})}{(3+\sqrt{7})(3-\sqrt{7})}$

(Rationalising the denominator)

$=\frac{2(3-\sqrt{7})}{(3{)}^2-(\sqrt{7}{)}^2}=\frac{2(3-\sqrt{7})}{9-7}$

$=\frac{2(3-\sqrt{7})}{2}=3-\sqrt{7}$

Now, $x-3=3-\sqrt{7}-3=-\sqrt{7}$

$\therefore (x-3{)}^2=(-\sqrt{7}{)}^2=7$