The difference of the squares of the two consecutive even natural numbers is $92$ . Taking x as the smaller of the two numbers, form an equation in x and hence find the large of the two

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Solution

$\begin{matrix} l e t t w o c o n s c u t i v e e v e n n u m b e r i s (2 x), (2 x + 2) \Rightarrow {(2 x + 2)}^{2} - {(2 x)}^{2} = 92 \Rightarrow 4 {(x + 1)}^{2} - 4 (x^{2}) = 92 \Rightarrow 4 [(x + 1 - x) (x + 1 + x)] = 92 \Rightarrow 1 \times (2 x + 1) = 23 \Rightarrow 2 x = 22 \Rightarrow x = 11 t h e n t h e n u m b e r i s (2 x + 2) = 22 + 2 = 24 \end{matrix}$

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