Question

x^4+x^2+1/x^2-4x-5 >0
Solve this ​

Answer 1

Step-by-step explanation:

x^2-4x+5=0

x

2

−

4

x

+

5

=

0

1) half the coefficient of x

x

square, add and subtract to balance

color(blue)(x^2-4x+2^2)+5-2^2=0

x

2

−

4

x

+

2

2

+

5

−

2

2

=

0

"2) the blue terms form a perfect square"

2) the blue terms form a perfect square

color(blue)((x-2)^2)+5-4=0

(

x

−

2

)

2

+

5

−

4

=

0

(x-2)^2+1=0

(

x

−

2

)

2

+

1

=

0

3) solve for x

x

(x-2)^2=-1

(

x

−

2

)

2

=

−

1

x-2=+-sqrt(-1)

x

−

2

=

±

√

−

1

x-2=+-i

x

−

2

=

±

i

:.x=2+-i