Question

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

Answer 1

Please ignore my answer above:

The answer is as follows:

Let the cubes of numbers are 2x3, 3x3  and4x3

(2x)3+ (3x)3+ (4x)3= 33957

8x3 + 27 x 3+ 64x3= 33957

=> 99x3= 33957

=> x3=33957/99

= x3= 343

x=7

The numbers are

Ist numbe is 2x= 2*7=14

2nd number is 3x = 3*7 = 21

3rd number is 4x = 4*7 = 28

Answer 2

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