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

Mathematics
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xy = 1 x - y = 5/6
solve for 1 variable, either x or y, and then use that value to evaluate for the other, then compare the two variables.
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.

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