Question

the sum of the squares of two consecutive positive even integars is 100. find the integars​

Answer 1

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Let x and (x+2) be the consecutive even integers.

We get

x^2+(x+2)^2=100

expanding, we get

x^2+x^2+4x+4=100

setting = 0, we get

2x^2+4x−96=0

Dividing by 2 , we get,

x^2+2x−48=0

factoring, we get,

(x+8)(x−6)=0

solving for x, we get

x+8=0 = x=−8

and x−6=0=x=6.

so, we have

(−8,−6) OR (6,8)