Question

The difference of two numbers is 4, the difference of their reciprocals is 4/21 find the two numbers

Answer 1

Let the first number be 'X', so the other number will be '(X+4)'.

$\because \frac{1}{x}-\frac{1}{x+4}=\frac{4}{21}$

$\frac{x+4-x}{x^2+4x}=\frac{4}{21}$

On simplifying further,

$X^2+4X-21=0$

On applying Sreedhracharya formula

$\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$\frac{-4\pm \sqrt{16-4\left(1\right)(-21)}}{2\left(1\right)}$

$\frac{-4\pm \sqrt{16+84}}{2\left(1\right)}$

$\frac{-4\pm \sqrt{100}}{2}$

$\frac{-4\pm 10}{2}$

$\therefore X=-7orX=3$

$\therefore$ The numbers are -7 & -3 or 3 & 7.