Question

The difference between the squares of two consecutive numbers is 31.Find the numbers

Answer 1

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$Given \: that : The \: difference \: of \: the \: squares \: of \: two \: consecutive \: number \: is \: 31 \\ \\ Let \: the \: first \: consecutive \: \: number \: = x \\ \\ Let \: the \: second \: consecutive \: number \: = x + 1 \\ \\ Now, \: \: Acc.to.Statement \: \\ \\ = > {(x + 1)}^{2} - {x}^{2} = 31 \\ \\ = > {x}^{2} + 1 + 2x - {x}^{2} = 31 \\ \\ = > 2x = 30 \\ \\ = > x = 15 \\ \\ So, \\ The \: first \: consecutive \: number \: is \: 15 \\ and \: Second \: consecutive \: number \: is \: 16$
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