Question

the sum of two numbers is 8 and the sum of their reciprocal is 8\15 find the numbers

Answer 1

Here is your answer, mark me as brainly

Answer 2

Answer:

$\large{\underline{\boxed{\sf 5 \: and \: 3}}}$

Step-by-step explanation:

Given that -

The sum of two numbers is 8 and the sum of their reciprocal is 8\15.

Let the numbers be x and y respectively.

Sum of numbers is 8.

⇒ x + y = 8.... (i)

⇒ y = 8 - x .... (ii)

Sum of reciprocals is 8/15.

⇒ $\dfrac{1}{\text{x}} + \dfrac{1}{\text{y}}= \dfrac{8}{15}$.... (iii)

Now, on solving (iii),

$\dfrac{1}{\text{x}} + \dfrac{1}{\text{y}}= \dfrac{8}{15} \\ \\ \frac{ \text {x + y }}{ \text{xy}} = \frac{8}{15} \\ \\ \bf on \: cross \: multiplying : \\ \\15( \text{x + y) = 8xy}$

Putting the value of (i) and (ii) here, we get -

$15 * 8 = 8 \text{x(8 - x)} \\ \\ \implies 15 = \text{x(8 - x)} \\ \\ \implies 15 = 8 \text{x - x}{}^{2} \\ \\ \implies \text{x} {}^{2} - 8\text x + 15 \\ \\ \implies \text{x} {}^{2} - 5\text{x - 3x} + 15 = 0 \\ \\ \implies \text{x(x - 5) - 3(x - 5) = 0 } \\ \\ \implies \text{(x - 5)(x - 3) = 0} \\ \\ \boxed{\therefore \bf x = 5 \: or \: x = 3}$

Hence, the required numbers are 5 and 3.