SOLUTION: [n/(n+1)] ² + [n/(n-1)] ² = 12 Find n.

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Question 1206697: [n/(n+1)] ² + [n/(n-1)] ² = 12
Find n.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!


%28n%2F%28n%2B1%29%29%5E2+%2B+%28n%2F%28n-1%29%29%5E2+=+12
n%5E2%2F%28n%2B1%29%5E2+%2B+n%5E2%2F%28n-1%29%5E2+=+12



n%5E2%28n-1%29%5E2%29+%2B+n%5E2%28n%2B1%29%5E2+=+12%28%28n%2B1%29%5E2%2A%28n-1%29%5E2%29

2+n%5E4+%2B2n%5E2++=+12n%5E4+-+24n%5E2+%2B+12...divide by 2

n%5E4+%2Bn%5E2++=+6n%5E4+-+12n%5E2+%2B+6

6n%5E4+-+12n%5E2+%2B+6-n%5E4+-n%5E2+=0

5n%5E4+-+13n%5E2+%2B+6++=0

5n%5E4+-+10n%5E2-3n%5E2+%2B+6++=0

%285n%5E4+-+10n%5E2%29-%283n%5E2+-+6+%29+=0

5n%5E2%28n%5E2+-+2%29-3%28n%5E2+-+2+%29+=0

%28n%5E2+-+2%29+%285n%5E2+-+3%29+=+0

if %28n%5E2+-+2%29++=+0=> n%5E2=2 => n=sqrt%282%29 or n=-sqrt%282%29
if %285n%5E2+-+3%29+=+0=> 5n%5E2=3+=> n=sqrt%283%2F5%29 or n=-sqrt%283%2F5%29

solutions:
n=sqrt%282%29
n=-sqrt%282%29
n=sqrt%283%2F5%29
n=-sqrt%283%2F5%29