Question

If the sum of 3 conjugate to numbers in a geometric progression is 26 and the sum of their squares is 364 then the product of those numbers is

Answer 1

Answer:

216

Step-by-step explanation:

Let the numbers be a, b, c.

As they are in geometric progression, b/a = c/b => ac = b².

The product of the three numbers is then abc = (ac)b = b²b = b³.  This is what we need to find.

Their sum is 26 and the sum of their squares is 364

=> a+b+c = 26   and   a²+b²+c² = 364

So

26² = (a+b+c)² = (a²+b²+c²) + 2(ab+bc+ca) = 364 + 2(ab+bc+ca)

=> 2(ab+bc+ca) = 26² - 364 = 676 - 364 = 312

=> ab+bc+ca = 156

=> ab+bc+b² = 156

=> (a+b+c)b = 156

=> 26b = 156

=> b = 6

=> b³ = 6³ = 216

=> abc = 216