Question

Please solve with proper steps

Answer 1

Final Answer :x = y


Steps:
1)
$log(2) + \frac{1}{2} log(x) + \frac{1}{2} log(y) = \\ log(x + y) \\ = > log( 2) + \frac{1}{2} log(xy) = log(x + y) \\ = > log(2) = log( \frac{x + y}{ \sqrt{xy} } ) \\ = > x + y = 2 \sqrt{xy} \\ = > {(x + y)}^{2} = 4xy \\ = > {x}^{2} - 2xy + {y}^{2} = 0 \\ = > {(x - y)}^{2} = 0 \\ = > x = y$