Question

If x2
– 5x + 1 = 0, then

(x^10+1)/x^5
has the value​

Answer 1

x

2

−5x+1=0

∴x

2

+1=5x

∴x+

x

1

=5

∴x

2

+

x

2

1

=25−2=23

∴x

3

+

x

3

1

=(x+

x

1

)

3

−3(x+

x

1

)

∴x

3

+

x

3

1

=125−15

∴x

3

+

x

3

1

=110

Now (x

3

+

x

2

1

)(x

3

+

x

3

1

)=56×23

∴x

5

+x+

x

1

+

x

5

1

=110×23

∴x

5

+

x

5

1

=2530−5

∴x

5

+

x

5

1

=2525.

hope it will help you dear.