Question

The sum of two numbers is 8 and the sum of their reciprocals is 8/15

Answer 1

Step-by-step explanation:

so what you need ? question is incomplete

Answer 2

Your Answer:

Given:-

• The sum of two numbers is 8
• The sum of their reciprocal is 8/15

To find:-

• The numbers

Solution:-

Let the numbers be x and y.

We have

$\tt x+y =8 \rightarrow \rightarrow\rightarrow \rightarrow (1)$

and

$\tt \dfrac{1}{x}+\dfrac{1}{y} =\dfrac{8}{15}\rightarrow \rightarrow\rightarrow \rightarrow (2)$

Solving equation 2, more further.

$\tt \dfrac{x+y}{xy} = \dfrac{8}{15}\\\\ \tt From \:\:equation\: \: 1\\\\ \tt \Rightarrow \dfrac{8}{xy}=\dfrac{8}{15} \\\\ \tt\Rightarrow xy=15\\\\ \ttFrom \: here\:\\\\ x=\dfrac{15}{y}\rightarrow\rightarrow\rightarrow\rightarrow(3)$

Putting value of x in Equation 1

$\tt \dfrac{15}{y}+y=8 \\\\ \tt \Rightarrow \dfrac{15+y^2}{y} = 8 \\\\ \Rightarrow \tt y^2-8y+15=0 \\\\\tt \Rightarrow y^2-(5+3)y+15=0 \\\\ \tt \Rightarrow y^2-5y -3y+15=0\\\\ \tt\Rightarrow y(y-5)-3(y-5)=0\\\\ \Rightarrow (y-5)(y-3)=0$

Equating the factors with zero.

we get y=5 and y=3

In case 1

if y = 5

then x =3

In case 2

if y = 3

then x = 5

So, the numbers are 5 and 3