The sum of a number and four times its reciprocal is 5.Find possible values of the number.

Answer 1

the number --- x
its reciprocal --- 1/x

x + 4(1/x) = 5
times x

x^2 + 4 = 5x
x^2-5x + 4 = 0
(x-1)(x-4) = 0
x = 1 or x = 4

I leave it up to you to check them out.