Question

X + 1 beta 2 X + 3 barabar 3 beta 8

Answer 1

Step-by-step explanation:

α,β are the roots of x

2

−2x+4=0

⇒α+β=2,αβ=4

α

2

+β

2

=(α+β)

2

−2αβ

=2

2

−2(4)

=4−8=−4

α

3

+β

3

=(α+β)

3

−3αβ(α+β)

=2

3

−3(4)(2)

=8−24=−16

Now, α

5

+β

5

=(α

3

+β

3

)(α

2

+β

2

)−α

3

β

2

−α

2

β

3

=(α

3

+β

3

)(α

2

+β

2

)−(αβ)

2

(α+β)

=(−16)(−4)−(4)

2

(2)

=64−32=32