Question

Factorize:- y^4+5y^2+9=0​

Answer 1

Answer:

Simplifying

y4 + 5y2 + 9 = 0

Reorder the terms:

9 + 5y2 + y4 = 0

Solving

9 + 5y2 + y4 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.

9 + 5y2 + -9 + y4 = 0 + -9

Reorder the terms:

9 + -9 + 5y2 + y4 = 0 + -9

Combine like terms: 9 + -9 = 0

0 + 5y2 + y4 = 0 + -9

5y2 + y4 = 0 + -9

Combine like terms: 0 + -9 = -9

5y2 + y4 = -9

The y term is 5y2. Take half its coefficient (2.5).

Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.

5y2 + 6.25 + y4 = -9 + 6.25

Reorder the terms:

6.25 + 5y2 + y4 = -9 + 6.25

Combine like terms: -9 + 6.25 = -2.75

6.25 + 5y2 + y4 = -2.75

Factor a perfect square on the left side:

(y2 + 2.5)(y2 + 2.5) = -2.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.