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