Question

If log (x² + y²) = log 2 +log x+
log y show that x=y​

Answer 1

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$\bf{(i)} \: log( {x}^{2} + {y}^{2}) = log2 + logx + logy \\ \rightarrow \bf{log( {x}^{2} + {y}^{2} )} = log2xy \\ \rightarrow \bf {x}^{2} + {y}^{2} = 2xy \\ \rightarrow \bf {x}^{2} - 2xy + {y}^{2} = 0 \\ \rightarrow \bf {(x - y)}^{2} = 0 \\ \rightarrow \bf x - y = 0 \\ \rightarrow \bf x = y$