The sum of a number and five times its reciprocal is 4.5. Write a quadratic equation for the number, and use the quadratic formula to find two such numbers.
+128475 Let n be the number and we have that
n + 5/n = 4.5 multiply through by n
n^2 + 5 = 4.5n rearrange as
n^2 - 4.5n + 5 = 0
Using the quad formula we have
n = 4.5 + √ [ 4.5^2 - 4*1*5 ] 4.5 + √[20.25 - 20] 4.5 + √ .25 4.5 + .5
___________________ = ________________ = __________ = _______ =
2 2 2 2
5/2 = 2.5
And the other solution is 4.5 - .5
_______ = 4/2 = 2
2
