Three numbers are in ratio 2- 3- 4 the sum of there cubes is 3397 find the number s

Dear student I think there is a small correction in the question In the question,the sum of cubes is given as 3397 but i think its 33957 because it is a questio ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard VIII

Mathematics

Cube-Root of Product of Numbers

Three numbers...

Question

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

Open in App

Solution

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 = $\frac{33957}{99}$ = 343
⇒x = $\sqrt[3]{343}$ = 7
Therefore, the numbers are: 2x = 2×7 = 14
3x = 3×7 = 21
4x = 4×7 = 28

Suggest Corrections

Similar questions

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

Three numbers are in ratio 2:3:4. The sum of their cubes is 0.334125. Find the numbers.

Q. Three numbers are in the ratio

2 : 3 : 4

to one another. The sum of their cubes is

0.334125

. Find the numbers.

Three numbers are in the ratio $2 : 3 : 4$ . The sum of their cube is $33957.$ Find the number.

Three numbers are in the ratio 1 : 2 : 3. The sum of their cubes is 98784. Find the numbers.

Join BYJU'S Learning Program

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

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 = 3395799 = 343 ⇒x =3√343= 7Therefore, the numbers are: 2x = 2×7 = 14 3x = 3×7 = 21 4x = 4×7 = 28

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 = $\frac{33957}{99}$ = 343
⇒x = $\sqrt[3]{343}$ = 7
Therefore, the numbers are: 2x = 2×7 = 14
3x = 3×7 = 21
4x = 4×7 = 28