Question

the sum of the cubes of three numbers is in the ratio 1:2:3 is 17,576. find the numbers. please tell me quickly tomorrow is my exam..!!​

Answer 1

Given: The sum of the cubes of three numbers is in the ratio 1:2:3 is 17,576.

To find: The numbers.

Solution:

Let the three numbers be equal to x, y and z. So according to the question, an equation can be formed as follows.

$x^{3} + y^{3} + z^{3} = 17576$

Given the ratios of the cubes, y and z can be equated to x as follows.

$\frac{x^{3} }{y^{3}} = \frac{1}{2}$

$y^{3} = 2x^{3}$

$\frac{x^{3}}{z^{3}} = \frac{1}{3}$

$z^{3} = 3x^{3}$

Now, the first equation can be written by replacing y³ by 2x³ and z³ by 3x³.

$x^{3} + 2x^{3} + 3x^{3} = 17576$

$6x^{3} = 17576$

$x = 14.31$

Now, the rest of the numbers can be calculated as follows.

$y^{3} = 2x^{3}$

$y = 18.03$

$z^{3} = 3x^{3}$

$z = 20.64$

Therefore, the numbers are 14.31, 18.03 and 20.64.

Answer 2

Numbers are 13 ,  13∛3  , 13∛4  if sum of the cubes of three numbers in the ratio 1:3:4 is 17,576.

Given:

• cubes of three numbers  in the ratio 1:2:3
• Sum of cubes of numbers is 17,576

To Find:

• Numbers

Solution:

Step 1:

Assume that cubes of the Numbers are x³ , 2x³ and 3x³ as ratio is 1:2:3

Numbers are  x , x∛2  , x∛3

Step 2:

Find Sum of the cubes

x³ + 2x³ + 3x³ = 6x³

Step 3:

Equate sum with given  17,576 and solve for x:

6x³ = 17576

=> x³ = 17576/6

=> x ≈ 14.3

Looks issue with Data.

Correct Data can be Ratio as 1 : 3 : 4  then cubes of the Numbers are x³ , 3x³ and 4x³

Numbers are x ,  x∛3  , x∛4

(x)³ + 3(x)³ + 4(x)³ = 8x³ = 17576

=> x³ = 2197

=> x = 13

Numbers are 13 ,  13∛3  , 13∛4

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