Question

Three numbers are in the ratio two is to 3 is to 4 of their cube 33957 find the numbers

Answer 1

let numbers be 2x,3x and 4x

⇒(2x)³ + (3x)³ + (4x)³ = 33957

⇒8x³ + 27x³ + 64x³ = 33957

⇒99x³ = 33957

⇒x³ = 33957/99 = 343

⇒x = ∛343 = 7

2x = 2×7 = 14

3x = 3×7 = 21

4x = 4×7 = 28

Answer 2

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

according to question

${(2x)}^{3} + {(3x)}^{3} + {(4x)}^{3} = 33957 \\ 8{x}^{3} + 27 {x}^{3} + 64 {x}^{3} = 33957 \\ 99 {x}^{3} = 33957 \\ {x}^{3} = \frac{33957}{99} \\ {x}^{3} = 343 \\ x = \sqrt[3]{343} \\ x = \sqrt[3]{ {(7)}^{3} } \\ x = 7$

Then , the three numbers are

$2x = 2 \times 7 = 14$

$3x = 3 \times 7 = 21$

$4x = 4 \times 7 = 28$