Question

product of 3 consecutive numbers is 64 find their mean proportional​

Answer 1

let the 3 concecutive numbers be x, x+1 ,x+2

According to the question

(x) × (x+1) × (x+2)

64 = (x^2 + x) × (x+2)

64 = x^2 (x + 2) + x (x + 2)

64 = x^3 + 2x^2 + x^2 + 2x

64 = x^3 + 3x^2 + 2x

0 = (x^3 + 3x^2) + (2x - 64)

= x^2 (x+3) + 2 (x-32)

= (x^2 + 2) + (x + 3) + (x-32)

therefore

x = root -2. not possible

x = -3

x = 32

therefore x can be -3 or 32