Answer:
x = ±√5i or x = ±i is solution of given equation.
Explanation:
We have given an equation.
x⁴+6x²+5 = 0
We to solve it using substitution.
Let u = x²
then, u² = x⁴
Putting above value in given equation , we have
u²+6u+5 = 0
Now, use method of factorization.
split the middle term of above equation
u²+5u+u+5 = 0
u(u+5)+1(u+5) = 0
(u+5)(u+1) = 0
Applying zero product property , we have
u+5 = 0 or u+1 = 0
u = -5 or u = -1
Putting u = x² in above equation, we have
x² = -5 or x² = -1
Taking square root of both sides of equations, we have
x = ±√-5 or x = ±√-1
x = ±√5i or x = ±i where i = √-1.