Question

*> If α, ß are the roots of equation 2x²-5x+1=0 2n and Sn = 2²n + ß²n, then prove that 4 S2021 + S2019 2019 = 21. 2020

Answer 1

Answer:

Let roots of 2x

2

−5x+1=0 be α,β

⇒α+β=

2

5

;αβ=

2

1

Let roots of x

2

+5x+2=0 be γ,δ

⇒γ+δ=−5;γδ=2

−(

αβ

α+β

)=−(

2

1

2

3

)=−5

⇒−

α

1

−

β

1

=−5

and −

α

1

×

β

−1

=

αβ

1

=

2

1

1

=2.

Explanation:

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