Question

Sum of two natural numbers is 8 and the difference of their reciprocal is 2/15. find the numbers.​

Answer 1

Answer:

Let 1st no. be x and 2nd be 8−x.

By the given condition,

$\sf \pink \implies \purple{ \dfrac{1}{x} - \dfrac{1}{8 - x} = \dfrac{2}{15}}$

$\sf \blue \implies \green{ \dfrac{8 - x - x}{ x (8 - x)} = \dfrac{2}{15}}$

$\sf \red \implies \orange{ \dfrac{8 - 2x}{8x - {x}^{2} } = \dfrac{2}{15}}$

$\sf \blue{Now,}$

$\sf \purple \implies \pink {120 - 30x = 16x - 2 {x}^{2}}$

$\sf \green \implies \blue{{2x}^{2} - 46x + 120 = 0}$

$\sf \orange \implies \red {{x}^{2} - 23x + 60 = 0}$

$\sf \pink \implies \purple {x(x - 20) - 3(x - 20) = 0}$

$\sf \blue \implies \green{(x - 3)(x - 20) = 0}$

$\sf \red \implies \orange{x = 3 \: or \: x = 20 \: is \: not \: possible}$

$\sf \purple{Therefore,}$

$\sf \pink{ {1}^{st} number = 3}$

$\sf \blue{{2}^{nd} number = 8 - 3 = 5}$

Answer 2

Answer:

Sum of two natural numbers is 8 and the difference of their reciprocal is 2/15. find the numbers.