Given that, α+β=1,αβ=−1 Let α,β be roots of quadratic equation, then the quadratic equation be x2−x−1=0 Now, α2−α−1=0 ⇒α2=α+1⋅⋅⋅⋅⋅⋅⋅(i) Similarly, β2=β+1⋅⋅⋅⋅⋅⋅⋅(ii) Multiply αn−1 in Eq. (i), we get αn+1=αn+αn−1⋅⋅⋅⋅⋅⋅⋅(iii) Multiply βn−1 in Eq. (ii), we get βn+1=βn+βn−1⋅⋅⋅⋅⋅⋅⋅(iv) Add Eqs. (iii) and (iv), we get αn+1+βn+1=(αn+βn)+(αn−1+βn−1) pn+1=pn+pn−1 29=pn+11 ⇒Pn=18 pn2=(18)2=324