56.4k views
0 votes
X^6 8=0 please helppp I’ll give u anything

User PALEN
by
9.5k points

1 Answer

2 votes

To solve the equation X^6 + 8 = 0, we can follow these steps:

Step 1: Subtract 8 from both sides of the equation to isolate the term with the variable:

X^6 = -8

Step 2: Take the sixth root of both sides to solve for X. The sixth root of a number is the number that, when raised to the power of 6, gives the original number:

X = (-8)^(1/6)

Step 3: Simplify the expression on the right side of the equation. Since (-8)^(1/6) is a complex number, it can be expressed in multiple ways. One common way is to write it in polar form:

X = 2 * cos((π + 2kπ)/6) + i * sin((π + 2kπ)/6)

where k is an integer ranging from 0 to 5.

Step 4: Evaluate the expression for each value of k to obtain all possible solutions. Substituting k = 0, 1, 2, 3, 4, 5 into the equation will give us the different values of X.

For example, when k = 0:

X = 2 * cos(π/6) + i * sin(π/6)

X = 2 * (√3/2) + i * (1/2)

X = √3 + i/2

Similarly, when k = 1:

X = 2 * cos(π/3) + i * sin(π/3)

X = 2 * (1/2) + i * (√3/2)

X = 1 + √3i/2

And so on, for k = 2, 3, 4, and 5.

These are the different solutions for the equation X^6 + 8 = 0. Each value of X corresponds to a complex number on the complex plane.To solve the equation X^6 + 8 = 0, we can follow these steps:

Step 1: Subtract 8 from both sides of the equation to isolate the term with the variable:

X^6 = -8

Step 2: Take the sixth root of both sides to solve for X. The sixth root of a number is the number that, when raised to the power of 6, gives the original number:

X = (-8)^(1/6)

Step 3: Simplify the expression on the right side of the equation. Since (-8)^(1/6) is a complex number, it can be expressed in multiple ways. One common way is to write it in polar form:

X = 2 * cos((π + 2kπ)/6) + i * sin((π + 2kπ)/6)

where k is an integer ranging from 0 to 5.

Step 4: Evaluate the expression for each value of k to obtain all possible solutions. Substituting k = 0, 1, 2, 3, 4, 5 into the equation will give us the different values of X.

For example, when k = 0:

X = 2 * cos(π/6) + i * sin(π/6)

X = 2 * (√3/2) + i * (1/2)

X = √3 + i/2

Similarly, when k = 1:

X = 2 * cos(π/3) + i * sin(π/3)

X = 2 * (1/2) + i * (√3/2)

X = 1 + √3i/2

And so on, for k = 2, 3, 4, and 5.

These are the different solutions for the equation X^6 + 8 = 0. Each value of X corresponds to a complex number on the complex plane.

User Manoj Madanmohan
by
9.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories