SOLUTION: The number obtained by adding the squares of a number and its reciprocal is greater by 7/4 than the sum of the number and its reciprocal. Find the number.

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Question 1067585: The number obtained by adding the squares of a number and its reciprocal is greater by 7/4 than the sum of the number and its reciprocal. Find the number.
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
highlight_green%28x%5E2%2B%281%2Fx%29%5E2-%28x%2B1%2Fx%29=7%2F4%29


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x%5E2%2B1%2Fx%5E2-x-1%2Fx=7%2F4, best common denominator is 4x%5E2.

4x%5E2%2Ax%5E2%2B4x%5E2%281%2Fx%5E2%29-4x%5E2%2Ax-4x%5E2%281%2Fx%29=4x%5E2%287%2F4%29

4x%5E4%2B4-4x%5E3-4x=7x%5E2

4x%5E4-4x%5E3-7x%5E2-4x%2B4=0
You can try checking possible roots of PLUS&MINUS of 1/4, 1/2, 1, 2, 4 according to Rational Roots Theorem and synthetic division. The only two REAL (and rational) roots found will be 1%2F2 and 2.

system%28x=2%2Cand%2C1%2Fx=1%2F2%29
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