SOLUTION: Find three consecutive positive even whole numbers such that the sum of the square of the two smaller numbers is 20 more than the square of the largest number?

Question 248484: Find three consecutive positive even whole numbers such that the sum of the square of the two smaller numbers is 20 more than the square of the largest number?
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
Let x, x+2 & x+4 be the 3 numbers.
x^2+(x+2)^2=(x+4)^2+20
x^2+x^2+4x+4=x^2+8x+16+20
2x^2+4x+4-x^2-8x-36=0
x^2-4x-32=0
(x-8)(x+4)=0
x-8=0
x=8 ans. for the smallest number.
8+2=10 ans. for the middle number.
8+4=12 ans. for the laegest number.
Proof:
8^2+10^2=12^2+20
64+100=144+20
164=164
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