# Three numbers are in the ratio 2:3:4. The sum of their cubes is 0.334125. How do you find the numbers?

##### 3 Answers

The 3 numbers are:

#### Explanation:

The question says there are three numbers but with a specific ratio. What that means is that once we pick one of the numbers, the other two are known to us through the ratios. We can therefore replace all 3 of the numbers with a single variable:

Now, no matter what we choose for

distributing the powers across the factors using

So the 3 numbers are:

The nos. are,

#### Explanation:

Reqd. nos. maintain ratio

By what is given,

So, the nos. are,

This soln. is in

I leave it to you to verify if complex roots satisfy the given cond. - hoping that you'll enjoy it!

Slightly different approach.

#### Explanation:

We have a ratio which is splitting the whole of something into proportions.

Total number of parts

Let the whole thing be

Then

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

We are told that the sum of their cubes is

Note that

( aren't calculators are wonderful!)

So

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Factor out the

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Take the cube root of both sides