Let `alpha` and `beta` be the roots of the equation `x^(2)-x-1=0` .If `p_(k)=(alpha)^(k)+(beta)^(k),k>=1` then which one of the following statements is not true?`

Let alpha,beta and gamma be the roots of the equation x^(3)-x-1=0 . If P_(k)=(alpha)^(k)+(beta)^(k)+(gamma)^(k),kge1 , then which one of the following statements is not true?

Let alpha,beta and gamma be the roots of the equation x^(3)-x-1=0 . If P_(k)=(alpha)^(k)+(beta)^(k)+(gamma)^(k),kge1 , then which one of the following statements is not true?

Let alpha and beta are the roots of x^2 – x – 1 = 0 such that P_k = alpha^k + beta^k , k ge 1 then which one is incorrect?

Let alpha and beta are the roots of x^2 – x – 1 = 0 such that P_k = alpha^k + beta^k , k ge 1 then which one is incorrect?

If alpha,beta are the roots of the equation x^2-2x+4=0 , find alpha^(n)+beta^(n) for (a) n=3k, k in N

If alpha and beta are the real roots of the equation x^(2)-(k+1)x-(k+2)=0, then minimum value of alpha^(2)+beta^(2) is

If alpha & beta are the roots of the quadratic equation x^(2)-(k-2)x-k+1=0 ,then minimum value of alpha^(2)+beta^(2) is

If alpha & beta are the roots of the quadratic equation x^(2)-(k-2)x-k+1=0 , then minimum value of alpha^(2)+beta^(2) is

If alpha,beta are the roots of the equation x^2-2x+4=0 , find alpha^(n)+beta^(n) for (a) n=3k, k in N (b) n ne 3k, k in N