SOLUTION: 6/p = 2 + p/p+1 using quadratic function

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Question 386826: 6/p = 2 + p/p+1 using quadratic function
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
6%2Fp+=+2+%2B+p%2F%28p%2B1%29
Use the common denominator, p%28p%2B1%29


%286%28p%2B1%29-2%2A%28p%28p%2B1%29%29-p%5E2%29%2F%28p%28p%2B1%29%29=0
%286p%2B6-2%2A%28p%5E2%2Bp%29%2Bp%5E2%29%2F%28p%28p%2B1%29%29=0
%286p%2B6-2p%5E2-2p-p%5E2%29%2F%28p%28p%2B1%29%29=0
%28-3p%5E2%2B4p%2B6%29%2F%28p%28p%2B1%29%29=0
%283p%5E2-4p-6%29%2F%28p%28p%2B1%29%29=0
The equation equals zero when the numerator equals zero.
3p%5E2-4p-6=0
3p%5E2-4p%2B4-6=4
Using the quadratic formula,
p+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
p+=+%284+%2B-+sqrt%28+%28-4%29%5E2-4%2A3%2A%28-6%29+%29%29%2F%282%2A3%29+
p+=+%284+%2B-+sqrt%28+16%2B72+%29%29%2F%286%29+
p+=+%284+%2B-+sqrt%28+88+%29%29%2F%286%29+
p+=+%284+%2B-+2%2Asqrt%28+22+%29%29%2F%286%29+
highlight%28p+=+%282+%2B-+sqrt%28+22+%29%29%2F%283%29+%29