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The sum of the squares of two consecutive even numbers is $452$. Find the numbers.
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Solution: Let the two consecutive even numbers be $x$ and $x + 2$.
A.T.Q.
$x^2 + (x + 2)^2 = 452$
$\Rightarrow x^2 + 2x - 224 = 0$
$\Rightarrow (x + 16)(x - 14) = 0$
$\Rightarrow x = 14$
Required numbers are $14$ and $16$.
A.T.Q.
$x^2 + (x + 2)^2 = 452$
$\Rightarrow x^2 + 2x - 224 = 0$
$\Rightarrow (x + 16)(x - 14) = 0$
$\Rightarrow x = 14$
Required numbers are $14$ and $16$.