Find all numbers such that the sum of the number and half its reciprocal is 57/40.

Answer 1

X + (1/2)(1/x) = 57/40

X + 1/(2x) = 57/40

2x^2 + 1 = (57/40)(2x)

2x^2 + 1 = (57/20)x

40x^2 + 20 = 57x

40x^2 - 57x + 20 = 0

( 8x - 5)( 5x - 4 )=0

x = 5/8 or x = 4/5

CHECK:

5/8 + 8/10 = (50+64)/80 = 114/80 = 57/40

4/5 + 5/8 = (32+25)/40 = 57/40