The sum of a number and its reciprocal is 25/12. Find the possible numbers

Question

Please help with full solution!!!! I need to hand this up tmr

Answer 1

X + 1/X = 25/12

X^2 +1 = 25X/12

X^2 -25X/12 = -1

X^2 -25X/12 + (25/24)^2 =-1 + (25/24)^2

(X - 25/24)^2 = 625//576 -1 = 49/576 = (7/24)^2

x- 25/24 = + or - 7/24

X = 25/24 + or - 7/24 = 18/24 or 32/24

X = 3/4 or 4/3

4/3 + 3/4 = 16/12 + 9/12 = 25/12