Question

if the product of two positive numbers is 1 and their difference is 5/6, then the larger number is ?

Answer 1

xy = 1
x - y = 5/6

Answer 2

solve for 1 variable, either x or y, and then use that value to evaluate for the other, then compare the two variables.

Answer 3

xy = 1 ------------> x = 1/y
x - y = 5/6 ------> x = 5/6 + y

Set the x's equal to each other.
1/y = 5/6 + y
1 = (5/6)y + y^2 ---------------> [Multiply both sides by y.]
0 = y^2 + (5/6)y - 1 ----------> [Subtract 1 from both sides.]
0 = 6y^2 + 5y - 6 -------------> [Multiply both sides by 6.]
0 = (3y - 2) (2y + 3) ---------> [Factor. Or use the quadratic formula.]
y = 2/3, (-3/2 isn't positive) ----> [Set (3y - 2) and (2y + 3) = 0 to solve for y.]

Substitute y = 2/3 into the first equation to solve for x:
x(2/3) = 1
x = 3/2

The larger number is 3/2.