If α,  β are the roots of the equation x2−px+q=0  and Un=αn+βn,  then pUn− qUn−1  is equal to

the given equation is x2−px+q=0 α,  β are the roots of given equationAnd given that, Un=αn+βn   From equation: α+β=p,  αβ=q Then pUn− qUn−1=(α+β)(αn+βn)−(αβ)(αn−1+βn−1) =αn+1+αβn+βαn+βn+1−αnβ−αβn =αn+1+βn+1=Un+1