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Q. If \( 6^{x-y} = 36 \) and \( 3^{x+y} = 729 \), find \( x^2 – y^2 \)
(a) 12 (b) 4 (c) 24 (d) 8
✏️ Solution
\( 6^{x-y} = 36 = 6^2 \Rightarrow x – y = 2 \)
\( 3^{x+y} = 729 = 3^6 \Rightarrow x + y = 6 \)
\( x^2 – y^2 = (x-y)(x+y) \)
\( = 2 \times 6 = 12 \)
Correct Option: (a) 12
\( \boxed{12} \)