SOLUTION: The sum of a number and its reciprocal is 89/40. find the number

Question 1060963: The sum of a number and its reciprocal is 89/40. find the number
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
let x be the number, then
:
x + 1/x = 89/40
:
(x^2 +1) / x = 89/40
:
cross multiply the fractions
:
40(x^2 +1) = 89x
:
40x^2 -89x +40 = 0
:
use quadratic formula
:
x = (-(-89) + square root( (-89)^2 -4*40*40) ) / (2*40) = 1.6 = 8/5
x = (-(-89) - square root( (-89)^2 -4*40*40) ) / (2*40) = 0.625 = 5/8
:
***********************
There are two solutions
:
x = 8/5, x = 5/8
***********************
:
check the solutions
:
x = 1.6 = 16/10 = 8/5
:
8/5 + 5/8 = 64/40 + 25/40 = 89/40, answer checks
:
625/1000 = 25/40 = 5/8
:
5/8 + 8/5 = 25/40 + 64/40 = 89/40, answer checks
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