The product of three numbers in gp is 216
Asked by admin @ in Math viewed by 381 People
the product of three numbers in G.P. is 216, but sum of their products in pairs is 156. find the numbers.
Answered by admin @
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
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