JEE Advanced 2017 Paper 2 Mathematics Q17

Mathematics

Problem

Read the following paragraph and answer Q.17 and Q.18. Let p,qp,q be integers and let α,β\alpha,\beta be the roots of the equation x2−x−1=0x^2-x-1=0, where α≠β\alpha\ne\beta. For n=0,1,2,…n=0,1,2,\ldots, let an=pαn+qβna_n=p\alpha^n+q\beta^n. FACT: If aa and bb are rational numbers and a+b5=0a+b\sqrt5=0, then a=0=ba=0=b. a12=a_{12}=

Browse the problem library