Question

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

Answer 1

Answer: The solutions are i and 5i.

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=√(-1)=i`

Similarly, put y = -5

`-5=x^2\\\\x=√(-5)=5i`

Hence, the solutions are i and 5i.

Answer 2

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

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