Question

Sum of two numbers is 24 and sum of their reciprocals are 1/6

Answer 1

Let the numbers be x and y .
ATQ
x+y=24..........................(1)
And
1/x + 1/y=1/6.................(2)
Solving equations 1 and 2
By substitution method
x=12,-12
Putting value of x in equation 1
y=12 and 36
Cheers

Answer 2

x+y=24 eq(1)
1/x+1/y =1/6
x+y=xy/6. eq(2)
Substracting eq(1) from eq(2)
x+y=24
-x-y=-xy/6
0=24-xy/6
xy/6=24
xy=144
x=144/y
Putting the value of x in eq(1)
144/y+y=24
144+y^2=24y
y^2-24y+144=0
y^2-(12+12)y+144=0
y^2-12y-12y+144=0
y(y-12) -12(y-12) =0
(y-12) (y-12) =0
(y-12) ^2=0
y=12, 12
Putting the value of x in eq(1)
12+x=24
x=12