Let x and y be two natural numbers such that x y = 12 ( x + y ) and x ≤ y . Then the total number of pairs ( x , y ) is

x y − 12 x − 12 y = 0 ⇒ ( x − 12 ) ( y − 12 ) = 144 Now 144 can be factorised into two factors x and y where x ≤ y and the factors are (1,144),(2,72),(3,48),(4,36),(6,24),(8,18) (9,16),(12,12) Thus there are eight solutions.

Mathematics - Quadratic Equation Question with Solution | TestHub

MathematicsQuadratic EquationInequationMedium2 minPYQ_2012

MathematicsMediumsingle choice

Let $x$ and $y$ be two natural numbers such that $x y = 12 (x + y)$ and $x \leq y$ . Then the total number of pairs $(x, y)$ is

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Solution:

$x y - 12 x - 12 y = 0 \Rightarrow (x - 12) (y - 12) = 144$ Now 144 can be factorised into two factors $x$ and $y$ where $x \leq y$ and the factors are (1,144),(2,72),(3,48),(4,36),(6,24),(8,18) (9,16),(12,12) Thus there are eight solutions.

Stream:JEESubject:MathematicsTopic:Quadratic EquationSubtopic:Inequation

⏱ 2mℹ️ Source: PYQ_2012

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