Question

three numbers are in the ratio 2 3 4 .the sum of their cube is 33957.find the largest number

Answer 1

Let the numbers be 2x, 3x and 4x
sum of cubes = 33957
⇒(2x)³ + (3x)³ + (4x)³ = 33957
⇒8x³ + 27x³ + 64x³ = 33957
⇒99x³ = 33957
⇒x³ = 33957/99 = 343
⇒x = ∛343 = 7

Numbers are:
2x = 2×7 = 14
3x = 3×7 = 21
4x = 4×7 = 28

Answer 2

Answer:

Let the numbers be 2x, 3x and 4x

sum of cubes = 33957

⇒(2x)³ + (3x)³ + (4x)³ = 33957

⇒8x³ + 27x³ + 64x³ = 33957

⇒99x³ = 33957

⇒x³ = 33957/99 = 343

⇒x = ∛343 = 7

Numbers are:

2x = 2×7 = 14

3x = 3×7 = 21

4x = 4×7 = 28