Question

Three numbers are in the ratio of 1:3:4. The sum of their cubes is 31556. Find the numbers

Answer 1

Let the numbers be x,3x and 4x.
x³+(3x)³+(4x)³=31556
x³+27x³+64x³=31556
92x³=31556
x³=343
x=7
Hence the first number is 7.
Then second number will be (3x)=(3*7)=21
Then third number will be (4x)=(4*7)=28

Answer 2

The numbers are 7, 21 and 28.

Step-by-step explanation:

According to the given information, it is given that there are three numbers and all the three numbers are in the ratio of 1:3:4.

Let the numbers according to the ratio be x, 3x and 4x, that is, let the first number be x, let the second number be 3x and let the third number be 4x.

Now, according to the given information, it is given that the sum of the cubes of the three numbers is 31556, which means that the sum of the cubes of x, 3x and 4x is 31556, that is the sum of x³, (3x)³ and (4x)³ is 31556, that is the sum of x³, 27x³ and 64x³ is 31556.

Then, we have,

x³ + 27x³ + 64x³ = 31556.

Taking x³ common, we get,

(1 + 27 + 64)x³ = 31556.

Or, 92x³ = 31556.

Or,  x³ = $\frac{31556}{92}$

Or, x³ = 343

Or, x = ∛343

Or, x = 7

Thus, x is equal to 7, the second number is equal to (3 * 7) = 21 and the third number is (4 * 7) = 28.

Thus, the numbers are 7, 21 and 28.

Learn more here

https://brainly.in/question/14021358

Learn more

https://brainly.in/question/37150902