Question

Q17. If x^4+1/x^4 = 727, find the values of:

(i) x^2+1/x^2

(ii) x −1/x

Answer 1

Answer:

x

4

+

x

4

1

=727

Adding 2 on both sides, we get

x

4

+

x

4

1

+2×x

2

×

x

2

1

=727+2

⇒(x

2

+

x

2

1

)

2

=27

2

Taking square root both sides, we get

x

2

+

x

2

1

=27

Subtracting 2 from both sides, we get

x

2

+

x

2

1

−2×x×

x

1

=27−2

⇒(x−

x

1

)

2

=5

2

Taking square root on both sides, we get

x−

x

1

=5