The difference between two natural numbers …
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Yogita Ingle 5 years, 11 months ago
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,
{tex}\frac{1}{x}-\frac{1}{x+5}=\frac{1}{10}{/tex}
{tex}\implies \frac{x+5-x}{x(x+5)}=\frac{1}{10}{/tex}
{tex}\implies \frac{x}{x^{2}+5x}=\frac{1}{5}{/tex}
Do the cross multiplication, we get
{tex}\implies 50=x^{2}+5x{/tex}
=> 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
0Thank You