Question

difference between the two numbers is 5 and difference between their reciprocals is 1/10then find the number​

Answer 1

Answer:

answer is one of the number is 5 and the other number is 10

Answer 2

AnswEr:

Let us Consider that two numbers be x and (x - 5).

Now, According to Question

$:\implies\tt\;\dfrac{1}{x - 5} - \dfrac{1}{x} = \dfrac{1}{10}$

$:\implies\tt\dfrac{x - (x - 5)}{x(x - 5)} =\dfrac{1}{10}$

$:\implies\tt\;\dfrac{5}{x(x -5)} = \dfrac{1}{10}$

$:\implies\tt\;x(x - 5) = 10$

$:\implies\tt\; x^2 - 5x - 50 = 0$

Now, Solving Quadratic Equation

$:\implies\tt\; x^2 - 5x - 50 = 0$

$:\implies\tt\; x^2 - 10x + 5x - 50 = 0$

$:\implies\tt\; x (x - 10) + 5 (x - 10) = 0$

$:\implies\tt\; (x - 10) (x + 5) = 0$

$:\implies\tt\;x - 10 = 0$

$:\implies\large\boxed{\sf{\pink{x = 10}}}$

$:\implies\tt\;x + 5 = 0$

$:\implies\large\boxed{\sf{\pink{x = -5}}}$

Since, Two numbers are - 5 and 10 and -5 is not possible.

$:\implies\tt\; x - 5$

$:\implies\tt\; 10 - 5 = 5$

So, The Numbers are 5 & 10.