The sum of the cubic powers of three rational numbers is -1009. The ratio between the first number and the second number is 2/3, and the ratio between the first number and the third number is 4/9. Find those numbers

Given:

The sum of the cubic powers of three rational numbers is -1009.

The ratio between the first number and the second number is .

The ratio between the first number and the third number is .

To find:

The three numbers.

Solution:

Let be the three numbers, then

               ...(i)

                       ...(ii)

                        ...(iii)

Using (i), (ii) and (iii), we get

On simplification, we get

Substituting in (ii), we get

Substituting in (iii), we get

Therefore, the three numbers are -4, -6 and -9 respectively.