Question

find the smallest number in a gp whose sum is 38 and product 1728.​

Answer 1

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Answer 2

Answer:

Let a/r, a, and ar be the three numbers in GP.

Sum, a/r + a + ar = 38 …(i)

Product, (a/r)a(ar) = 1728

a³= 1728

Taking cube root

a = 12

Substitute a in (i)

(12/r) + 12 + 12r = 38

(12/r) + 12r = 26

((1/r) + r) = 26/12

(r² + 1)/ r = 13/6

6r²-13r+6 = 0

Solving using the quadratic formula, we get

r = 2/3or 3/2

The numbers will be 18, 12, 8 or 18, 12, 8.

The smallest number is 18.