Question

Find three consecutive odd numbers the product of which is 148 more than the cube of their middle number.

Answer 1

The numbers are
`-39,-37,-35`

Explanation:

Let

x-----> the first odd number

x+2----> the middle odd number

x+4---> the third odd number

`x(x+2)(x+4)=(x+2)^(3) +148`

`(x^(2)+2x)(x+4)=(x^(2)+4x+4)(x+2)+148\\x^(3)+4x^(2)+2x^(2)+8x=x^(3)+2x^(2)+4x^(2)+8x+4x+8+148\\x^(3)+6x^(2)+8x=x^(3)+6x^(2)+12x+156\\8x=12x+156\\4x=-156\\x=-39`

The numbers are

`x=-39`

`x+2=-39+2=-37`

`x+4=-39+4=-35`