Question

The continued product if three numbers in G.P is 216, and the sum of the ptoducts of them in pairs is 156; find the numbers.


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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

Answer 2

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Ans

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