SOLUTION: Find three consecutive integers where the sum of the first two equals the square of the third minus 146.

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Question 149570: Find three consecutive integers where the sum of the first two equals the square of the third minus 146.
Answer by Fombitz(13823) About Me  (Show Source):
You can put this solution on YOUR website!
We'll define three consecutive integers A,B,C
A=N
B=N%2B1
C=N%2B2
Now add the conditions,
A%2BB=C%5E2-146
Substitute for values and solve for N.
N%2BN%2B1=%28N%2B2%29%5E2-146
2N%2B1=N%5E2%2B4N%2B4-146
N%5E2%2B2N-143=0
You can factor this quadratic equation,
N%5E2%2B2N-143=%28N%2B13%29%28N-11%29=0
First factor solution:
N%2B13=0
N=-13
A=-13
B=-12
C=-11
.
.
.
Second factor solution:
N-11=0
N=11
A=11
B=12
C=13