The sum of the squares of two consecutive positive even numbers is 452
Question:

The sum of the squares of two consecutive positive even numbers is 452. Find the numbers.

Solution:

Let the two consecutive positive even numbers be x and (x + 2).

According to the given condition,

$x^{2}+(x+2)^{2}=452$

$\Rightarrow x^{2}+x^{2}+4 x+4=452$

$\Rightarrow 2 x^{2}+4 x-448=0$

$\Rightarrow x^{2}+2 x-224=0$

$\Rightarrow x^{2}+16 x-14 x-224=0$

$\Rightarrow x(x+16)-14(x+16)=0$

$\Rightarrow(x+16)(x-14)=0$

$\Rightarrow x+16=0$ or $x-14=0$

$\Rightarrow x=-16$ or $x=14$

∴ x = 14             (x is a positive even number)

When x = 14,
x + 2 = 14 + 2 = 16

Hence, the required numbers are 14 and 16.

 

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