SOLUTION: find all possible value of n for which the equation x^2+x-n=0 has integral solution.

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Question 329890: find all possible value of n for which the equation x^2+x-n=0 has integral solution.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Look for solutions that look like,
x%5E2%2Bx-n=%28x%2Ba%29%28x%2Bb%29=0 where a and b are integers.
Using the FOIL method,
x%5E2%2Bx-n=x%5E2%2B%28a%2Bb%29x%2Bab
Comparing,
1.a%2Bb=1
2.ab=-n
From eq. 1,
b=1-a
Substituting into eq. 2,
a%281-a%29=-n
highlight%28n=a%28a-1%29%29 where a is any integer.
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Two examples:
a=0,b=1,n=0
x%5E2%2Bx=x%28x%2B1%29=0
solutions:x=-a=0,x=-b=-1
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a=5,b=-4,n=5%284%29=20
x%5E2%2Bx-20=%28x%2B5%29%28x-4%29
solutions:x=-a=-5,x=-b=4
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