Question

If the sum and its reciprocal is 10/3 then the numbers are

Answer 1

If the sum and its reciprocal is 10/3
   x + 1/ x = 10 / 3
 (x^2 + 1) / x  = 10 / 3
 3( x^2 + 1) = 10 x
 3 x^2 - 10 x + 3 = 0
 3 x^2 -9 x - x + 3 = 0
3 x(  x - 3) -1 (x - 3) = 0
(3 x - 1)(x - 3) = 0
3 x - 1 = 0 & x - 3 = 0
 x = 1/3  ,  3
so the numbers are 1/3 & 3

Answer 2

x+1/x=10/3

x^2+1/x=10/3

3(x^2+1)=10x

3x^2+3-10x=0

3x^2-10x+3=0

3x^2-9x-x+3=0

3x(x-3)-(x-3)=0

(3x-1)(x-3)=0

x=1/3 , x=3