Question

If x= 3−√13/2 , what is the value of x power of 2 + 1/ to the power 2​

Answer 1

Answer:

x=

2

3−

13

and

x

1

=

3−

13

2

.

We know, (x+

x

1

)

2

=x

2

+

x

2

1

+2

and x

2

+

x

2

1

=(x+

x

1

)

2

−2.

Now, x+

x

1

=

2

3−

13

+

3−

13

2

=

2(3−

13

)

(3−

13

)

2

+4

=

2(3−

13

)

9+13−6

13

+4

=

2(3−

13

)

26−6

13

=

2(3−

13

)

2

13

(

13

−3)

.

So x+

x

1

=−2

13

and (x+

x

1

)

2

=4×13=52.

x

2

+

x

2

1

=(x+

x

1

)

2

−2

=52−2=50.