Question

Three numbers are in G.P., and their sum and product are respectively 63 and 1728. Find
them.​

Answer 1

Step-by-step explanation:

a(ar)(ar²) = 1728

a³r³ = 12³

ar = 12

a + ar + ar² = 63

a + 12 + ar² = 63

a(1+r²) = 51

(12/r) ( 1+r²) = 51

12/r + 12r = 51

(1/r + r) = 51/12 = 17/4

(1+r²)/r = 17/4

4 + 4r² = 17r

4r² - 17r + 4 = 0

4r² - 16r - r + 4 = 0

4r(r - 4) - 1(r - 4) = 0

r = 4 , 1/4

when r = 4 , then a = 3

when r = 1/4 , then a = 48

The numbers are

3 , 12 , 48