1.

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

Answer»

Answer:

x=24 and y=3

Step-by-step explanation:

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

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

•Verification:

x³+y³

=(3)³+(6)³

=27+216

=243

=RHS

Here,LHS=RHS=243

Hence, VERIFIED


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