Question

Find the possible real numbers x, x+2, and x+8 such that the reciprocal of the smallest number is the sum of the reciprocals of the other two.

Answer 1

1/x =1/(x+2) + 1/(x+8)

(x+2)(x+8) = x(x+8) + x(x+2)
x^2 + 10 x + 16 = x^2 + 8 x + x^2 + 2 x
x^2 -16 = 0
x = +/- 4
check to see if both work