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Q. \( 6^{x-y} = 36,\quad 3^{x+y} = 729 \)
✏️ Solution
\( 36 = 6^2 \)
\( 6^{x-y} = 6^2 \Rightarrow x-y = 2 \)
\( 729 = 3^6 \)
\( 3^{x+y} = 3^6 \Rightarrow x+y = 6 \)
\( x^2 – y^2 = (x-y)(x+y) \)
\( = 2 \times 6 \)
\( = 12 \)
\( \boxed{12} \)