Question

the sum of two no is 9 and the sum of their reciprocal is 1/2

Answer 1

let the nos be x and y.
given,
X+y= 9
so, y= 9- x( eqn 1)
ATQ,
1÷ x+1÷ y= 1/2
(y+x)÷xy = 1/2
( y+ x) 2= xy
2y+ 2x= xy
2(9- x)+2x=x(9 - x)
18- 2x+ 2x = 9x- x^2
18 = 9x- x^2
x^2- 9 x + 18= 0
x^2- 6x- 3x+ 18= 0
X( x-6) - 3(x-6)= 0
either x-3= 0 or x-6=0
x= 3 or x=6
putting x= 3or 6 in eqn 1,we get
y=9-3. or y= 9-6
y=6. or y = 3