Three numbers are in the ratio 2:3:4. The sum of their cubes is 0.334125. How do you find the numbers?
The 3 numbers are:
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,
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.
We have a ratio which is splitting the whole of something into proportions.
Total number of parts
Let the whole thing be
We are told that the sum of their cubes is
( aren't calculators are wonderful!)
Factor out the
Take the cube root of both sides