After solving the equations x^3 + y^3 = 243, the difference between the two numbers is found to be 3. Here option A is correct.
Let's denote the first number as x and the second number as y. The given information can be expressed as equations:
The cube of a number is 8 times the cube of another number:
x^3 = 8y^3
The sum of the cubes of the numbers is 243:
x^3 + y^3 = 243
Now, we need to find the difference of the numbers, which is |x - y|. We can try to solve these equations simultaneously to find the values of x and y.
Substitute the first equation into the second one:
8y^3 + y^3 = 243
Combine like terms:
9y^3 = 243
Divide by 9:
y^3 = 27
Take the cube root of both sides:
y = 3
Now, substitute y = 3 into the first equation to find x:
x^3 = 8(3)^3
x^3 = 8 * 27
x^3 = 216
Take the cube root of both sides:
x = 6
Now, find the difference |x - y|:
|6 - 3| = 3
Therefore, the correct answer is (a) 3.
Complete question:
The cube of a number is 8 times the cube of another number. If the sum of the cubes of numbers is 243, the difference of the numbers is:
(a) 3
(b) 4
(c) 6
(d) None of these