Question

three numbers are to one another 2:3:4. the sum of their cubes is 131769. find the smallest numbers.

Answer 1

Let the numbers be 2x,3x and 4x.
Given,
Sum of cubes=131769
We can write,
8x^3+27x^3 +64x^3=131769
or 99x^3=131769
or x^3= 131769÷ 99
or x^3=1331
or x=11
So,the numbers are 22,33,44.
the smallest number=22

Answer 2

Let the numbers be 2x, 3x, & 4x.

So, cube of these numbers will be 8x³, 27x³, 64x³ respectively.

A/Q,

➡ 8x³ + 27x³ + 64x³ = 131769

➡ 99x³ = 131769

➡ x³ = 131769/99

➡ x³ = 1331

➡ x = 11

So, the numbers are = 2x = 11*2 = 22

➡ 3x = 11*3 = 33

➡ 4x = 11*4 = 44.

Smallest no is 22.

So the required answer is 22.

Hope it will help you !!!