Find integers a and b such that x2-x-1 , divides ax17 + bx16 +1 = 0. please solve with full steps . Share with your friends Share 3 Anuradha Sharma answered this The given function is, Fx=ax17+bx16+1and let Px be a polynomial such that Pxx2-x-1=FxHere we can see that constant term of Px must be -1.Now we have, x2-x-1c1x15+c2x14+.....c15x-1=Fxwhere c15 is some coefficient . However, since Fx has no x term, it must be true thatc15=1Now we have to find c14 , here we can see that while finding this term we can left all other term, x2-x-1.....c14x2+x-1=something +0x2+spmethingThere fore on comaring here we get, c14=-2Similarily we can find other term in similar way,c13=3, c12=-5, c11=8 and we can see that it is a pattern with alternate +amd - sign with next term's magnitude is equal to sum of last two number that is nothing but fibonnaci series.therefore a=c1=F16, where F16 denotes the 16th Fibonnaci number anda=987 and b = -F17=1597 -7 View Full Answer
