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)
