1/x + 1/y = 7/12 xy = 12 find x and y

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Answer 1

The equations are 1/x + 1/y = 7/12 and xy = 12.

Equation 2 : xy = 12 ⇒ y = 12/x.

Equation 1 : 1/x + 1/y = 7/12 ⇒ (y + x)/xy = 7/12.

Substitute the values of xy = 12 and y = 12/x in (y + x)/xy = 7/12.

[(12/x) + x]/12 = 7/12

12/x + x = 7

12 + x² = 7x

x² - 7x + 12 = 0

x² - 4x - 3x + 12 = 0

x(x - 4) - 3(x - 4) = 0

(x - 3)(x - 4) = 0

Apply zero product property : If a*b = 0, then either a = 0, b = 0 or both a and b are zeros.

x = 3 and x = 4

If x = 3 then y = 12/x ⇒ y = 12/(3) = 4.

If x = 4 then y = 12/x ⇒ y = 12/(4) = 3.

The values of (x, y) = (3, 4) or (4, 3).