Let the common ratio be r







Divide both sides by 3


Use the principle of even roots:





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

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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