Question

the sum of two numbers is 15 if sum of receprocals is 3 by
10 find the number​

Answer 1

Answer:

Step-by-step explanation:

Given :-

Sum of two numbers = $\bf{15}$

Reciprocal of two numbers = $\bf{\frac{3}{10}}$

To Find :-

The Numbers

Solution :-

Let the 1st number be x.

And the 2nd number be 15 - x.

$\bf {\underline {According \: to \: the \: Question}}$

$\sf\implies\frac{1}{x}+\frac{1}{15-x}=\frac{3}{10}$

$\sf\implies \frac{15}{15-x^2}=\frac{3}{10}$

$\sf\implies 150=45x-3x^2$

$\sf\implies 3x^2-45x+150=0$

$\sf\implies x^2-15x+50=0$

$\sf\implies x^2-5x-10x+50=0$

$\sf\implies (x-10)(x-5)=0$

$\bf{\implies x=10 \: \: and \: \: x=5}$

Hence, The numbers are 10 and 5.