Question

the sum of two no.s is 8 and 15 times the sum of their reciprocal is also 8. find the numbers .

Answer 1

x+y=8----(1)
>y=8-x----(2)
15{(1/x)+(1/y)}=8
$\frac{x + y}{xy} = \frac{8}{15}$
$\frac{8}{xy} = \frac{8}{15} \: \: from(1)$
xy=15
x(8-x)=15 from (2)
x²-8x+15=0
x²-3x-5x+15=0
x(x-3)-5(x-3)=0
x=3 or 5 sub. in (2)
y=5 or 3
so the no. are 5,3.
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