Question

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

Answer 1

Answer:

Required numbers are 5, 10

Explanation:

It is given that, difference of two natural numbers is 5

Let the x, (x+5) are two natural numbers.

Reciprocals of the numbers are

x and 1/(x+5)

According to the problem given,

$\frac{1}{x}-\frac{1}{x+5}=\frac{1}{10}$

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

$\implies \frac{x}{x^{2}+5x}=\frac{1}{5}$

Do the cross multiplication, we get

$\implies 50=x^{2}+5x$

=> x²+5x-50=0

Splitting the middle term, we get

=> x²+10x-5x-50=0

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

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

=> x+10 = 0 Or x-5=0

=> x = -10 Or x = 5

But the two numbers are natural numbers.

x = 5

Therefore,

Required two natural numbers are,

x = 5

and

x+5 = 5+5 = 10

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Answer 2

Answer:

Your answer is 5 and. 10