SOLUTION: the sum of a number and its reciprocal is 34/15

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Question 479631: the sum of a number and its reciprocal is 34/15
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Let the number be n and its reciprocal 1%2Fn

given:
the sum of a number and its reciprocal is 34%2F15

n%2B+%281%2Fn%29+=34%2F15.....multiply thru by n

n%5E2+%2B1+=+%2834%2F15%29n.....multiply thru by 15

15n%5E2+%2B15+=+34n

15n%5E2+%2B15+-34n=0.....use quadratic formula

n+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+.........a=15, b=15 and c=-34
n+=+%28-15+%2B-+sqrt%28+15%5E2-4%2A15%2A%28-34%29+%29%29%2F%282%2A15%29+
n+=+%28-15+%2B-+sqrt%28+225%2B2040+%29%29%2F30+

n+=+%28-15+%2B-+sqrt%28+2265+%29%29%2F30+
n+=+%28-15+%2B-+47.59%29%2F30+

solutions:
n+=+%28-15+%2B+47.59%29%2F30+
n+=+%2832.59%29%2F30+
n+=+1.086+.......its reciprocal is n+=+1%2F1.086=0.92
or
n+=+%28-15+-+47.59%29%2F30+
n+=+%28-62.59%29%2F30+
n+=+-2.086+.......its reciprocal is n+=+-1%2F2.086=-0.48