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
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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
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