Question

Three numbers are in the ratio 2:3:4. The sum of their cubes is 33957. Find the numbers.​

Answer 1

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

Answer 2

Given,

$&#x21AA$Three numbers are in the ratio 2:3:4.

$&#x21AA$Their cubes is 33957.

To find,

The numbers.

Solution:-

Let the numbers be $(2x)$,$(3x)$,$(4x)$

A/Q

$8x³$+$27x²$+$64x²$=$33957$

$99x³=33957$

${x}^3$=$\frac{33957}{9}$

${x}^3$=$343$

$x$=$&#8731{343}$

$x$=$\cuberoot{7×7×7}$

$x=7$

Therefore the numbers are:-

i)$2x=2×7=14$

ii)$3x=3×7=21$

iii)$4x=4×4=28$

The numbers are:-$14,21,28$