Question

Three numbers are in ratio 2:3:4.The sum of their cubes is 33957,then greatest number is

Answer 1

let the three number be 2x 3x and 4x
according to questions

$8 {x}^{3} + 27 {x}^{3} + 64 {x}^{3} = 33957 \\ 99 {x}^{3} = 33957 \\ {x}^{3} = \frac{33957}{99} \\ x = \sqrt[3]{343} \\ x = 7$
hence the greatest number is 4x7= 28

Answer 2

Answer:

Given :-

The ratio of three no.s = 2:3:4

The sum of their cubes = 33957

To find :-

The numbers = ?

Solution :-

Let the three no.s given in the ratio be :-

2x, 3x, 4x

According to the ques..,

${(2x)}^{3} + {(3x)}^{3} + {(4x)}^{3} = 33957$

${8x}^{3} + {27x}^{3} + {64x}^{3} = 33957$

${99x}^{3} = 33957$

${x}^{3} = \dfrac{33957}{99}$

${x}^{3} = 343$

$x = \sqrt[3]{343}$

$x = \sqrt[3]{7 \times 7 \times 7 }$

$x = 7$

The value of x = 7

The three numbers are :-

2x = 2 × 7 = 14

3x = 3 × 7 = 21

4x = 4 × 7 = 28