Question

If x^2 − 4x + 1 = 0, find the value of x^4 +1/x^4

Answer 1

Answer:

Solution

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Correct option is

C

52

Given that x

2

−4x+1=0

⇒x

2

+1=4x

⇒

x

(x

2

+1)

=

x

4x

{dividing both sides with x}

⇒(x+

x

1

)=4...(1)

Now, we know that (x+

x

1

)

3

=x

3

+(

x

1

)+3x

2

x

1

+3x+

x

1

=x

3

+

x

3

1

+3x+

x

3

⇒(x+

x

1

)

3

=x

3

+

x

3

1

+3(x+

x

1

)

OR x

3

+

x

3

1

=(x+

x

1

)

3

−3(x+

x

1

)...(2)

From (1) x+

x

1

=4, Substitute in (2)

We will get x

3

+

x

3

1

=4

3

−3.4

=4(4

2

−3)

=4.13

=52