The sum of the squares of two consecutive positive even integers is 340. How do you find the number?

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Answer 1 · 2018-04-10T05:25:41

The numbers are $12$ $12$ and $14$ $14$

To find the answer, set up an equation.

Set $x$ $x$ equal to the lower number, and $x + 2$ $x+2$ as the higher number since they are consecutive even numbers so they are two apart.

Now write out the equation according to the question

${(x)}^{2} + {(x + 2)}^{2} = 340$ $(x)^2+color(blue)((x+2))^2 = 340$

$x^{2} + x^{2} + 4 x + 4 = 340$ $x^2 + color(blue)(x^2 + 4x + 4) = 340$

Combine like terms.

$2 x^{2} + 4 x + 4 = 340$ $2x^2 + 4x + 4 = 340$

Set equal to zero so you can factor.

$2 x^{2} + 4 x - 336 = 0$ $2x^2 + 4x -336 = 0$

$(2 x + 28) (x - 12) = 0$ $(2x+ 28)(x-12) = 0$

$x = - 14, 12$ $x= -14, 12$

$x = 12$ $x=12$ because the answer must be positive according to the question.

That means $x + 2$ $x+2$ is 14.

You can double check:

${(12)}^{2} + {(14)}^{2} = 340$ $(12)^2 + (14)^2= 340$

$144 + 196 = 340$ $144+196=340$

$340 = 340$ $340=340$