Question

the product of three numbers in GP in 216 and the sum of the product of them in pair is 126 .
find the number??
please solve???

Answer 1

Let a/r , a , ar are in GP

A/C to question,
(a/r ) × a × ar = 216
a³ = 216
a³ = (6)³
a = 6

again,
sum of their products in pair = 156
(a/r ) × a + a × ar + ar × (a/r) = 156
a²/r + a²r + a² = 156
36/r + 36r + 36 = 156
36( 1/r + r + 1) = 156
3(r² + r + 1) = 13r
3r² + 3r + 3 - 13r = 0
3r² -10r + 3 = 0
3r² - 9r - r + 3 = 0
r = 3 and 1/3

so, numbers are 6/3, 6 , 6×3 => 2, 6, 18
numbers are 6×3 , 6 , 6/3 => 18, 6, 2