Answer: The number = 3 /4 or 4 / 3
Concept:
Here, we need to know the idea of a reciprocal.
Reciprocal is also called the multiplicative inverse. It is similar to turning the number upside down which is found by interchanging the numerator and denominator.
Number ⇒ Reciprocal = 1 / Number
Solve:
STEP ONE: Set up the equation
Let x = the number
Let 1 / x = the reciprocal
x + 1 / x = 25 / 12
STEP TWO: Multiply x on both sides
(x + 1 / x) · x = (25 / 12) · x
x² + 1 = 25x / 12
STEP THREE: Multiply 12 on both sides
(x² + 1) × 12 = (25x / 12) × 12
12x² + 12 = 25x
STEP FOUR: Subtract 25x on both sides
12x² + 12 - 25x = 25x - 25x
12x² - 25x + 12 = 0
STEP FIVE: Solve for the quadratic equation
(3x - 4) (4x - 3) = 0 ⇔ (Factorization of the equation)
(x - 4 / 3) (x - 3 / 4) = 0
x = 4 / 3 or x = 3 / 4
Hope this helps!! :)
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