Question

three positive numbers are such that the product of the first and the second is 1 / 2, that of the second and third is 2 / 3 and that of the first and the third is 3 / 4.find the numbers.

Answer 1

Let the three numbers be x,y,z
Given product of first and second is 1/2
Product of second and third is 2/3
Product of first and third is 3/4
According to given
x * y =1/2
y=1/2x

y * z =2/3
1/2x * z =2/3
z=4x/3

x * z =3/4
x *4x/3 =3/4
x^2=9/16
x=3/4

y=1/2x
y=1/2*4/3
y=2/3

z=4x/3
z=(4*3)/(4*3)
z=1

Therefore the three numbers are 3/4 , 2/3 , 1