Question 357926
3,a,b,c,768
<pre>

Let the common ratio be r

{{{a = 3r}}}
{{{b = ar = (3r)r = 3r^2}}}
{{{c = br = (3r^2)r = 3r^3}}}
{{{768 = cr = (3r^3)r = 3r^4}}}

{{{768=3r^4}}}
Divide both sides by 3
{{{256=r^4}}}

Use the principle of even roots:

{{{"" +- root(4,256)=r}}}

{{{"" +- 4 = r}}}

If r = +4, then

a = 3r = 3(+4) = 12

b = ar = 12(+4) = 48

c = br = 48(+4) = 192

and as a check:

768 = cr = 192(4) = 768  so that checks.

So one solution is a=12, b = 48, c = 192

---------------------------------------

If r = -4, then

a = 3r = 3(-4) = -12

b = ar = -12(-4) = 48

c = br = 48(-4) = -192

and as a check:

768 = cr = -192(-13) = 768,so that checks too.

So the other solution is a=-12, b = 48, c = -192

There are two solutions.

Edwin</pre>