Question

The sum of two no is 8 determine the no if the sum of there reciprical is 8/15

Answer 1

Hey friend, Harish here.

Here is your answer:

Let the numbers be x,y.

Then,

⇒ $(x+y)=8$

⇒ $\frac{1}{x} + \frac{1}{y} = \frac{8}{15}$

⇒ $\frac{x+y}{xy} = \frac{8}{15}$

Now substitute x + y value in above equation. Then,

⇒ $\frac{8}{xy} = \frac{8}{15}$

Now, 8 on both sides get canceled.

Then,

$xy = 15$

As x+ y = 8 & xy = 15.

Then, x & y must be 3 , 5.

CHECK:

x + y = 3 + 5 = 8.

xy = 3 x 5 = 15.
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Hope my answer is helpful to you.

Answer 2

Let the no. be x and y

• Sum of two no. is 8

x + y = 8 .... ( i )

• Sum of their reciprocal is 8/15

$\frac{1}{x} + \frac{1}{y} = \frac{8}{15}$


$\frac{y + x}{xy} = \frac{8}{15}$

Putting value of x + y = 8 from ( i )

$\frac{8}{xy} = \frac{8}{15}$


$\frac{1}{xy} = \frac{1}{15}$


xy = 15 ..... ( ii )

From ( i )

x + y = 8

x = 8 - y

Putting value of x in ( ii )

xy = 15

( 8 - y ) y = 15

8y - y² = 15

y² - 8y + 15 = 0

y² - 5y - 3y + 15 = 0

y ( y - 5 ) - 3 ( y - 5 ) = 0

( y - 5 ) ( y - 3 ) = 0

• ( y - 5 ) = 0

y = 5

• ( y - 3 ) = 0

y = 3

=> x = 8 - y

When y = 5
x = 3

When y = 3
x = 5