Find all ordered triples (a,b,c) that meet the following conditions...

Question

1. The sum of the three numbers is 158
2. the product of the three numbers is 74088
3. b=ar and c=ar^2 for some real values of r

Answer 1

a+b+c = 158

abc = 74088

b = ar and c = ar^2

Then

a+ar+ar^2 = 158

a(1+r+r^2) = 158

a = 158/(1+r+r^2) <---- will use this equation

a(ar)(ar^2) = 74088

a^3*r^2 = 74088

(158/(1+r+r^2))^3 * r^2 = 74088

3944312/ (1+r+r^2)^3 * r^2 = 74088

3944312*r^2 = 74088*(1+r+r^2)^3

0 = 74088*(1+r+r^2)^3 - 3944312*r^2

Per desmos.com the solutions are

r = -3.325

r=-0.116

r=0.184

r=1.593

Then you use the equation noted above to find a.

From there you can find b and c, since b = ar and c = ar^2