Question

The difference to two numbers is 5 and the difference of their reciprocal is 1 by 10 . Find the number

Answer 1

HEYA MATE, HERE IS UR ANSWER

Let the two numbers be x and y .

According to the question

x-y=5

x=5+y------(1)

and $\frac{1}{x}-{1}/{y}$=$\frac{1}{10}$-------(2)

Substituting x=5+y

$\frac{1}{5+y}-{1}/{y}$=$\frac {1}{10}$

y+5+y/(5+y)y=1/10

2y+5/y^2+5y=1/10

By cross multiplication

10 (2y+5)=y^2+5y

20y+50=y^2+5y

0=y^2+5y-20y-50

0=y^2-15y-50

Now let us find the factors of 50 such that a ×b=50 and a+b=15

So such factors are 10 and 5

0=y^2-(10+5)y-50

0=y^2-10y-5y-50

0=y (y-10)+5 (y-10)

0=(y+5)(y-10)

$<b><i><u>Case 1 </u></i></b>$
y+5=0
y=-5
x=5+(-5)
x=5-5
x=0

$<b><i><u>Case 2 </u></i></b>$
y-10=0
y=10
x=5+10
x=15

$\mathbb{Be\:Brainly }$

Answer 2

Answer:

Step-by-step explanation:

Solution :-

Let the 1st required natural number be x.

And the 2nd natural number be (x - 5).

Then,

x > x - 5

⇒ 1/x < 1/x - 5

⇒ 1/x - 5 > 1/x

According to the Question,

⇒ 1/x - 5 - 1/x = 1/10

⇒ x - (x - 5)/(x - 5)x = 1/10

⇒ 5/(x - 5)x = 1/10

By cross multiplication,

⇒ (x - 5)x = 50

⇒ x² - 5x - 50 = 0

⇒ 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, - 5 (As x can't be negative)

⇒ x = 10

1st Number = x = 10

2nd Number = x - 5 = 10 - 5 = 5

Hence, the required natural numbers are 10 and 5.