Question

give the answer with proof

Answer 1

Howdy !!

your answer is ----

Let, x be the first number and y be the second number ..

so , according to the given condition

x + y = 9 .......(1)

and 1/x + 1/y = 9/14 .....(2)

considered equation (2)

1/x + 1/y = 9/14

=> x+y/xy = 9/14

=> 9/xy = 9/14 ....[ from (1) ]

=> xy = 14 => x = 14/y

put this value in equation (1) , we get

14/y + y = 9
=> 14 + y^2 = 9y

=> y^2 - 9y + 14 = 0
now, factories it --

=> y^2 -7y-2y+14 = 0

=> (y-7) (y-2) = 0

=> y = 7 , 2

when , y = 7
then from (1)
x+7 = 9
=> x = 2

when , y = 2
then from (1)
x+2 = 9
=> x = 7

so, the two number is 2 & 7

hope it help you