Question

What are the solutions of the equation x4+6x^2+5=0? Use substitution to solve

Answer 1

Answer:

+ or - square root of 5, and + or - i

Step-by-step explanation:

(x^2 + 5)(x^2 + 1)= 0

Set each set of parentheses equal to zero:

x^2 + 5 = 0; x^2 = -5, so x will equal plus or minus i times the square root of 5.

X^2 +1 = 0; x^2 = -1, so x will equal plus or minus i times the square root of one, which is just i

Answer 2

Answer: The solutions are i and 5i.

Step-by-step explanation:

Since we have given that

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

By using Substitution, we use

$y=x^2$ in the above equation:

$y^2+6y+5=0\\\\y^2+5y+y+5=0\\\\y(y+5)+1(y+5)=0\\\\(y+1)(y+5)=0\\\\y=-1,-5$

Now, put the value of y in the equation $y=x^2$.

Put y = -1,

$-1=x^2\\\\x=\sqrt{-1}=i$

Similarly, put y = -5

$-5=x^2\\\\x=\sqrt{-5}=5i$

Hence, the solutions are i and 5i.