Class 10

Math

All topics

Quadratic Equations

The sum of two numbers is $15$. If the sum of their reciprocal is $(103 )$, then find the numbers.

Let one of the numbers be $x$.

Other number is $(15−x)$

Sum of their reciprocals $=103 $

$x1 +15−x1 =103 $

$(15−x_{2})15 =103 $

$150=45x−3x_{2}$

$3x_{2}−45x+150=0$

$x_{2}−15x+50=0$

$(x−10)(x−5)=0$

$x=10$ or $5$

Therefore, the numbers are $10$ and $5$.