Question

Three numbers are in the ratio 1:2:3 amd the sum of the cubes is 3,34,125 . find the numbers.
please solve this ​

Answer 1

Answer:

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:

2:3:4⇒2x:3x:4x

Now, no matter what we choose for x we get the three numbers in the ratios specified. We are also told the sum of the cubes of these three numbers which we can write:

(2x)3+(3x)3+(4x)3=0.334125

distributing the powers across the factors using (a⋅b)c=acbc we get:

8x3+27x3+64x3=99x3=0.334125

x3=0.33412599=0.003375

x=3√0.003375=0.15

So the 3 numbers are:

2⋅0.15,3⋅0.15,4⋅0.15⇒0.3,0.45,0.6