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The difference of two perfect cubes is 386. If the cube root of the smaller of the two numbers is 7, then the cube root of the larger number is​

Respuesta :

Hrishii

Answer:

9

Step-by-step explanation:

Let the two perfect cubes be x and y where x > y.

According to the given conditions:

[tex] {x}^{3} - {y}^{3} = 386...(1) \\ y = 7...(2) \\ plug \: y = 7 \: in \: equation \: (1) \\ {x}^{3} - {7}^{3} = 386 \\ {x}^{3} - 343 = 386 \\ {x}^{3} = 343 + 386 \\ {x}^{3} = 343 + 386 \\ {x}^{3} = 729 \\ x = \sqrt[3]{729} \\ x = 9[/tex]

Thus the cube root of the larger number is 9.

Building and solving an equation, it is found that the cube root of the larger number is 9.

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  • Examples of perfect cubes are 1, as [tex]1^3 = 1[/tex], 8, as [tex]2^3 = 8[/tex], 27, as [tex]3^3 = 27[/tex], and so on...
  • We do not know the numbers, so they are called [tex]x^3[/tex] and [tex]y^3[/tex].
  • Since the difference is 386, we have that:

[tex]x^3 - y^3 = 386[/tex]

  • The cube root of the smaller number is 7, thus, [tex]y = 7[/tex], and now, it is possible to solve for x, and find the cube root of the larger number.

[tex]x^3 - y^3 = 386[/tex]

[tex]x^3 - 7^3 = 386[/tex]

[tex]x^3 - 343 = 386[/tex]

[tex]x^3 = 386 + 343[/tex]

[tex]x^3 = 729[/tex]

[tex]x = \sqrt[3]{729}[/tex]

[tex]x = 9[/tex]

Thus, the cube root of the larger number is 9.

A similar problem is given at https://brainly.com/question/13161078

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