Question

If $6^{x-y}=36$ and $3^{x+y}=729$, then find $x^2-y^2$.

• A. 12
• B. 4
• C. 24
• D. 8

Answer 1

Answer: (A)

$6^{x-y}=36$
$6^{x-y}=6^2$
$\therefore x-y=2$
$\text{ and }{3}^{x+y}=3^6\Rightarrow x+y=6$
From equations (1) and (2), we get $x^2-y^2=12$