Question

the sum of two numbers is 9 and the sum of their reciprocal is 1/2 find the numbers

Answer 1

Heya

Let the numbers be x and y

x+y=9

x=9-y

According to the problem,

1/x + 1/y = 1/2

(x+y)/xy = 1/2

9/xy = 1/2

xy = 18

(9-y)y = 18

9y-y²-18=0

y²-9y+18 = 0

y²-6y-3y+18=0

y(y-6)-3(y-6)=0

(y-6)(y-3)=0

The numbers are 3 and 6

Answer 2

let the two numbers be x & y.
so, according to the question

eqn 1) x + y = 9

eqn 2) 1/x + 1/y = 1/2

by simplifying eqn 2, we will get

eqn 3) y+x/xy = 1/2
by cross multiplication
2(x+y) = xy.........final eqn 3.

so now as the value of x+y is 9 from eqn
1st than,
2(9) = xy
xy = 18
x = 18/y

so putting the value of x in eqn 1st
x + y = 9
18/y +y = 9
18+y^2 =9y
y^2-9y+18=0

by splitting middle term
y^2-6y-3y+18
y(y-6)-3(y-6)
(y-3)(y-6)
y=3 & y=6

so the two no.s are 3&6.

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