Find two consecutive even positive integers,if sum of their squares is 580.
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The sum of the squares of two consecutive even integers is 580.
What are the integers?
:
x^2 + (x+2)^2 = 580
x^2 + x^2 + 4x +4 = 580
2x^2 + 4x + 4 - 580 = 0
2x^2 + 4x -576
Simplify, divide by 2
x^2 + 2x - 288 = 0
Factors to
(x+18)(x-16) = 0
x = 16 and 18 are the integers
What are the integers?
:
x^2 + (x+2)^2 = 580
x^2 + x^2 + 4x +4 = 580
2x^2 + 4x + 4 - 580 = 0
2x^2 + 4x -576
Simplify, divide by 2
x^2 + 2x - 288 = 0
Factors to
(x+18)(x-16) = 0
x = 16 and 18 are the integers
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