Question

If x^2+1/x^2=6,find the value of x^4+1/x^4

Answer 1

Step-by-step explanation:

x+

x

1

=6

⇒(x+

x

1

)

2

=x

2

+

x

2

1

+2x.

x

1

=x

2

+

x

2

1

+2

⇒x

2

+

x

2

1

=(x+

x

1

)

2

−2=6

2

−2=34

⇒(x

2

+

x

2

1

)

2

=x

4

+

x

4

1

+2x

2

.

x

2

1

=x

4

+x

4

+

x

4

1

+2

⇒x

2

+

x

2

1

=(x

2

+

x

2

1

)

2

−2=34

2

−2

=1154.

Hence, the answer is 1154.