Question

the difference of two numbers is 5 and the difference of their reciprocal is 1/10.find the numbér

Answer 1

Answer: The two numbers are 10 and 5..

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Answer 2

Answer:

Numbers can be 10 and 5

Numbers can be -5 and -10

Step-by-step explanation:

Let the number be x

Reciprocal of number= $\frac{1}{x}$

Since we are given that the difference of two numbers is 5.

So, second number = x-5

reciprocal = $\frac{1}{x-5}$

Since we are given that the difference of their reciprocal is 1/10

So, $\frac{1}{x} -\frac{1}{x-5} =\frac{1}{10}$

$x-5 -x=\frac{1}{10} \times(x)(x-5)$

$50=(x)(x-5)$

$x^2-5x-50=0$

$x^2-10x+5x-50=0$

$x(x-10)+5(x-10)=0$

$(x-10)(x+5)=0$

$x=10,-5$

If x = 10

So, numbers can be 10 and x-5=10-5=5

if x = -5

So, numbers can be -5 and x-5=-5-5=-10