Question

The difference between two numbers is 5 and there numbers difference between 1/10 . Than what is the number ​

Answer 1

$\huge\blue {\mathfrak{Bonjour Mate!}}$

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

••••

Answer 2

Hello Buddy ✌

Step-by-step explanation:

⇒1/x-5 – 1/x = 1/10

⇒x - (x-5)/x - (x-5) = 1/10

⇒5/x - (x-5) = 1/10

⇒ x(x-5) = 50

⇒ x2 - 5x - 50 = 0

⇒ x2 - 10x + 5x - 50 = 0

⇒ x (x - 10) + 5 (x - 10) = 0

⇒ (x+5) (x-10) = 0

⇒ (x+5) (x-10) = 0

⇒ x = -5 or 10

⇒ x = 10 (x = -5 , rejected)

∴ Two numbers are 10 and (10-5) = 5.