Question

What's the answer for this question x4 + 6x2 + 5 = 0

Answer 1

Answer:

x = i or x = -i or x = i sqrt(5) or x = -i sqrt(5)

Step-by-step explanation:

Solve for x:

x^4 + 6 x^2 + 5 = 0

Substitute y = x^2:

y^2 + 6 y + 5 = 0

The left hand side factors into a product with two terms:

(y + 1) (y + 5) = 0

Split into two equations:

y + 1 = 0 or y + 5 = 0

Subtract 1 from both sides:

y = -1 or y + 5 = 0

Substitute back for y = x^2:

x^2 = -1 or y + 5 = 0

Take the square root of both sides:

x = i or x = -i or y + 5 = 0

Subtract 5 from both sides:

x = i or x = -i or y = -5

Substitute back for y = x^2:

x = i or x = -i or x^2 = -5

Take the square root of both sides:

Answer: x = i or x = -i or x = i sqrt(5) or x = -i sqrt(5)