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The cube of number is 8 times the cube of another number. If the sum of the cubes of the numbers is 243, then find the difference of the number​

The cube of number is 8 times the cube of another number. If the sum of the cubes of the numbers is 243, then find the difference of the number​

Grade:11

1 Answers

Harshit Singh
askIITians Faculty 5963 Points
9 months ago
Dear Student

Let one number be x and the other number be y.

Given that,

Cube of one number is 8 times the cubes of other
x³=8y³.................(1)

Also,

Sum of the cube of these numbers is 243.
x³+y³=243......(2)

Now,

Solving the equation,

x³+y³=243

y³+8y³=243 [Using (1)]

9y³=243

y³=27

y=3

Substituting y=3 in (1),

x³ = 8y³

x³ = 8(3)³

x³ = 8(27)

x³ = 216

x = 6

Now,

Difference of the numbers:

x-y

=6-3

=3

Hence, the difference between both numbers is 3.

Thanks

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