Question

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

Answer 1

Answer:

Answer: Let the first number be x and the second number be y. According to the question, x^3=8*y^3 that implies x^3--8*y^3=0 also, x^3+y^3=243 on solving these two equations we get x=6 and y=3 so the difference between them is 3,

Answer 2

Step-by-step explanation:

AnswEr

Let's consider that two numbers are x & y.

⠀⠀⠀ $\underline{\boldsymbol{According\: to \:the\: Question :}}$⠀⠀⠀

⠀⠀⠀Cube of number is 8 times the cube of another number :

$:\implies\sf x^3 = 8y^3$⠀⠀⠀⠀⠀ -eq(1).

Sum of the cubes of the numbers is 243.

$:\implies\sf x^3 + y^3 = 243$ ⠀⠀ -eq(2).

⠀⠀⠀From both Equations :

$:\implies\sf 8y^3 + \cancel{ y^3} = 243 \\\\\\:\implies\sf x^3 +\cancel{ y^3} = 243 \\\\\\:\implies\sf \purple{9y^3 = 243}\\\\\\:\implies\sf y^3 = \dfrac{\cancel{243}}{\cancel{\: 9}} \\\\\\:\implies\sf y^3 = 27 \\\\\\:\implies\boxed{\frak{\pink{y = 3}}}$

⠀⠀

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀Substituting value of y in eq (1).

$:\implies\sf x^3 = 8y^3 \\\\\\:\implies\sf x^3 = 8(3)^3\\\\\\:\implies\sf x^3 = 8(27) \\\\\\:\implies\sf x^3 = 216\\\\\\:\implies\boxed{\frak{\pink{x = 6}}}$

⠀$\therefore$ Value of y & x is 3 & 6.

⠀$\bigstar$ Difference of the numbers :

$:\implies\sf Numbers = x - y \\\\\\:\implies\sf 6 - 3\\\\\\:\implies\boxed{\frak{\purple{3}}}$

⠀⠀Hence, Difference of the numbers is 3.