Question

Find three real numbers in GP whose sum is 30 and product is 216

Answer 1

Let the numbers be,

$\frac{a}{r},a,ar$

Given,

$\frac{a}{r}\times a\times ar=216$

$\Rightarrow a^3=216$

$\therefore a=6$

$\frac{a}{r}+a+ar=30$

$\frac{1}{r}+1+r=5$

$r^2-4r+1=0$

$r=2\pm \sqrt{3}$

Therefore the numbers are:

$\frac{6}{2\pm \sqrt{3}},6,12\pm 6\sqrt{3}$