Question

7. The cube of a number is 8 times the cube of another number .If the sum of the
cubes of the number is 243 , What is the difference of the numbers?​

Answer 1

Answer:

The numbers are 3 & 6

And their sum is 9

Explanation:

Given that,

The cube a number is 8 times the cube of another number.

Let's say, the number is ‘x’ and the another number is ‘y’

Cube of ‘x’ is 8 times the cube of ‘y’

⇒ x³ = 8y³ . . . .(i)

And also, it's given that sum of their cube is 243.

Then,

⇒ x³ + y³ = 243 . . . . .(ii)

Substitute eq.(i) in eq.(ii) :-

⇒ 8y³ + y³ = 243

⇒ 9y³ = 243

⇒ y³ = 243/9

⇒ y³ = 27

⇒ y = ³√27

⇒ y = 3

Substituting the value of ‘y’ in eq.(i) :-

⇒ x³ = 8y³

⇒ x³ = 8(3)³

⇒ x³ = 216

⇒ x = ³√216

⇒ x = 6

∴ The numbers are 3 & 6

Hence, their sum is :-

= 3 + 6

= 9

Answer 2

Answer:

2

Step-by-step explanation:

Let the numbers be x and y.

According to Question,

x³= 8y³_______a

³√x³= ³√8y³

x= 2y

x - 2y = 0______b

So, x=4 and y=2

Putting x = 4 and y = 2 in a,

So, (4)³= 8(2)³

64 = 8*8

64 = 64

For b,

4 - 2*2= 0

4 - 4 = 0

0 = 0

So, the difference between the two numbers= 4 - 2 = 2

Hence, proved