SOLUTION: The sum of the squares of the two larger of three consecutive even integers is 12 less than 4 time the square of the smaller one. Find the even number

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Question 994563: The sum of the squares of the two larger of three consecutive even integers is 12 less than 4 time the square of the smaller one. Find the even number
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
n is any integer.
The integers you want start as system%282n%2C2n%2B2%2C2n%2B4%29.

The transcribed description is %282n%2B2%29%5E2%2B%282n%2B4%29%5E2=-12%2B4%282n%29.
Solve for n, and evaluate your consecutive even integers.

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

The sum of the squares of the two larger of three consecutive even integers is 12 less than 4 time the square of the smaller one. Find the even number
Let smallest integer be S

Then others are: S + 2, and S + 4

We then get: %28S+%2B+2%29%5E2+%2B+%28S+%2B+4%29%5E2+=+4S%5E2+-+12

S%5E2+%2B+4S+%2B+4+%2B+S%5E2+%2B+8S+%2B+16+=+4S%5E2+-+12

2S%5E2+%2B+12S+%2B+20+=+4S%5E2+-+12

0+=+4S%5E2+-+2S%5E2+-+12S+-+12+-+20

0+=+2S%5E2+-+12S+-+32

2%28S%5E2+-+6S+-+16%29+=+2%280%29 ------- Factoring out GCF, 2

S%5E2+-+6S+-+16+=+0

(S - 8)(S + 2) = 0

S, or smallest integer = highlight_green%288%29               OR                highlight_green%28S+=+-+2%29



You should be able to find the others.