Problem: find the smallest number in gp whose sum is 38 and product is 1728
Rationale: "let x , y , z be the numbers in geometric progression ? y ^ 2 = xz x + y + z = 38 xyz = 1728 xyz = xzy = y ^ 2 y = y ^ 3 = 1728 y = 12 y ^ 2 = xz = 144 z = 144 / x x + y + z = x + 12 + 144 / x = 38 x ^ 2 + 12 x + 144 = 38 x x ^ 2 - 26 x + 144 = 0 ( x - 18 ) ( x - 8 ) = 0 x = 8,18 if x = 8 , z = 38 - 8 - 12 = 18 the numbers are 8,12 , 18 their sum is 38 their product is 1,728 the smallest number is 8 answer : d"
annotated_formula: multiply(divide(divide(divide(divide(38, const_1000), const_3), const_3), const_3), divide(divide(divide(divide(38, const_1000), const_3), const_3), const_3))