Problem 4. Recurence, induction. a) Find every x such that for every n 0we have xn+2 = 2xn+1 +xn. b) Sequence an satisfies the followingrecurrence: a0 = 0, a1 = 1, an+1 =2an+1 + an. Find b, c such thatan = bxn + cyn where x and y are found in parta). Solution take x^n common we have x^n( x^2 - 2x -1 ) = 0 so x = 0 is one solution or x^2 - 2x -1 = 0 x = 1+root 2 , root2 -1.