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  4. If 6x-y=36 and 3x+y=729, then find x2-y2.

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

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Solution:

$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 $x^2-y^2=12$