Question 37 of 157MediumMCQ
If α,β are the roots of the equation, x2−x−1=0 and Sn=2023αn+2024βn, then : Solutions · 1
Official solution
\[x2−x−1=0Sn=2023αn+2024βnSn−1+Sn−2=2023αn−1+2024βn−1+2023αn−2+2024βn−2=2023αn−2[1+α]+2024βn−2[1+β]=2023αn−2[α2]+2024βn−2[β2]=2023αn+2024βnSn−1+Sn−2=SnPutn=12S11+S10=S12\] Answer the question to unlock