SOLUTION: the sum of the squares of two consecutive positive even integers is 340. find the integers.

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Question 110013This question is from textbook algebra(structure and method)
: the sum of the squares of two consecutive positive even integers is 340. find the integers. This question is from textbook algebra(structure and method)

Answer by HyperBrain(694) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=the smaller integer
Then let x+2=the next integer

IF the sum of the squares of two consecutive positive even integers is 340, then:
x%5E2%2B%28x%2B2%29%5E2=340
x%5E2%2B%28x%28x%2B2%29%2B2%28x%2B2%29%29=340
x%5E2%2B%28%28x%5E2%2B2x%29%2B%282x%2B4%29%29=340
x%5E2%2B%28x%5E2%2B%282x%2B2x%29%2B4%29=340
x%5E2%2B%28x%5E2%2B4x%2B4%29=340
%28x%5E2%2Bx%5E2%29%2B4x%2B4=340
2x%5E2%2B4x%2B4=340
x%5E2%2B2x%2B2=170
x%5E2%2B2x%2B2-170=170-170
x%5E2%2B2x-168=0

BY the quadratic formula,
x=%28-2%2B-sqrt%282%5E2%2B4%2A1%2A168%29%29%2F%282%2A1%29
x=%28-2%2B-sqrt%284%2B672%29%29%2F%282%29
x=%28-2%2B-sqrt%28676%29%29%2F%282%29
x=%28-2%2B-26%29%2F%282%29
x=%28-2%2B26%29%2F2 or x=%28-2-26%29%2F%282%29
x=24%2F2=12 or x=-28%2F2=-14
If x=12, x+2=14
If x=-14, x+2=-12

Thus, the numbers maybe (12, 14) or (-14,-12)\

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HyperBrain!