Question

$a=-2+\sqrt{3}$ and $b=-2-\sqrt{3}$ then $\frac{1}{a^2}-\frac{1}{b^2}$ is

• A. $14$
• B. $-14$
• C. 0
• D. 1

Answer 1

Answer: (C)

0

Question seems incomplete. Presumed values for a & b and obtained solution. The answer (0) does not match the choices A or B. It seems additional choices C & D have not been captured.

Presume that

a = -2+$\sqrt{3}$

b = -2-$\sqrt{3}$

Since we need to derive value of $\frac{1}{a^2}-\frac{1}{b^2}$, substituting the values of a and b, we get following:

$\frac{1}{a^2}-\frac{1}{b^2}$ = ${\left(\frac{1}{-2+\sqrt{3}}\right)}^2+{\left(\frac{1}{-2-\sqrt{3}}\right)}^2$

$={(2-\sqrt{3})}^2+{(-2+\sqrt{3})}^2$

$=4+3-4\sqrt{3}-(4+3-4\sqrt{3})$

$=0$