Question

The sum of 2 nos is 8. And sum of their reciprocles is 8/15. Find the nos

Answer 1

Step-by-step explanation:

x+y=8---------1

1/x+1/y=8/15----2

by 2

=x+y/xy=8/15

8/xy=8/15

xy=15

x=15/y

15/y+y=8

y^2-8y+15

(y-5)(y-3)

when y=5 , x=3

when y=3 , x=5

Answer 2

Answer:

x=3or 5

y = 3 or 5

Step-by-step explanation:

let the numbers be x and y

ATQ

x+y=8, x=8-y

and

$\frac{1}{x} + \frac{1}{y} = \frac{8}{15} ...(i)$

putting x=8-y in (i) we get

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

$\frac{y + (8 - y)}{8 - y(y)} = \frac{8}{15}$

$\frac{8}{8y - {y}^{2} } = \frac{8}{15}$

$8(8y - {y}^{2} ) = 8 \times 15$

$64y - {8y}^{2} = 120$

${8y}^{2} - 64y + 120 = 0$

$or$

${y}^{2} - 8y + 15 = 0$

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

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

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

y=3 or y=5

Hence , x=8-y= 3 or 5

so, values of x and y may be 3 and 5 or 5 and 3.

HOPE IT IS HELPFUL.

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