Question

Find the three numbers in G.P. whose sum is 14 and whose
product is 64.​

Answer 1

Answer: 2, 4, 8

Explanation:

Let the numbers be
`(a)/(r), a, ar`

This means that:

1. 
   `(a)/(r)+a+ar=14`
2. 
   `\left((a)/(r) \right)(a)(ar)=64 \longrightarrow a^(3)=64 \longrightarrow a=4`

Substituting a=4 into the first equation,

`(4)/(r)+4+4r=14\\\\4+4r+4r^(2)=14r\\\\4r^(2)-10r+4=0\\\\2(2r-1)(r-2)=0\\\\r=(1)/(2), 2`

So, the numbers are
`(4)/(1/2), 4, 4\left((1)/(2) \right)`, or 2, 4, 8

• Note that whether you used r=1/2 or r=2, you would get the same answer, it's just that a/r and ar would take different values depending on which r you used.