Question

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

Answer 1

Answer: 2, 4, 8

Step-by-step explanation:

Let the numbers be $\frac{a}{r}, a, ar$

This means that:

1. $\frac{a}{r}+a+ar=14$
2. $\left(\frac{a}{r} \right)(a)(ar)=64 \longrightarrow a^{3}=64 \longrightarrow a=4$

Substituting a=4 into the first equation,

$\frac{4}{r}+4+4r=14\\\\4+4r+4r^{2}=14r\\\\4r^{2}-10r+4=0\\\\2(2r-1)(r-2)=0\\\\r=\frac{1}{2}, 2$

So, the numbers are $\frac{4}{1/2}, 4, 4\left(\frac{1}{2} \right)$, 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.