Question

If alpha and beta are the roots of x2+x+1=0, then alpha2 + beta2 =

Answer 1

Answer:

x

2

−x−1=0

α+β=1

and α.β=−1

Now,

2−α

1+α

+

2−β

1+β

=

4−2(α+β)+α.β

2−β+2α−αβ+2−α+2β−αβ

=

4−2(α+β)+α.β

4+α+β−2α.β

=

4−2−1

4+1+2

=7

And

2−α

1+α

2−β

1+β

=

4−2(α+β)+α.β

1+(α+β)+αβ

=

4−2−1

1+1−1

=1

Hence, the equation is

x

2

−7x+1=0.