The sum of the squares of two consecutive even integers is 452. find the two integers.
Mathematics · High School · Tue Nov 03 2020
Answered on
Let the first even integer be x
then, 2nd even integer is x+2
So, according to question
x^2 + (x+2)^2 = 452
x^2 + x^2 + 2(x)(2) + 2^2 = 452 { (a +b)^2 = a^2 + 2ab + b^2}
x^2 + x^2 + 4x + 4 = 452
2x^2 + 4x + 4 = 452
2x^2 + 4x + 4 - 452 =0
2x^2 + 4x - 448 = 0
x^2 + 2x -224 = 0
x^2 + 16x - 14x - 224 =0
x(x+16) -14(x+16) =0
(x-14) (x+16) =0
Let x - 14 =0
x =14
and, x + 16 =0
x= -16
So, the first even integer is 14 and second even integer is 16.