Let $$\alpha $$ and $$\beta $$ be the roots of the equation x² - x - 1 = 0.
If p_k = $${\left( \alpha \right)^k} + {\left( \beta \right)^k}$$ , k $$ \ge $$ 1, then which one of the following statements is not true?

Let $$\alpha $$ and $$\beta $$ be two real roots of the equation
(k + 1)tan²x - $$\sqrt 2 $$ . $$\lambda $$tanx = (1 - k), where k($$ \ne $$ - 1) and $$\lambda $$ are real numbers. if tan² ($$\alpha $$ + $$\beta $$) = 50, then a value of $$\lambda $$ is:

If $$\alpha $$, $$\beta $$ and $$\gamma $$ are three consecutive terms of a non-constant G.P. such that the equations $$\alpha $$x ² + 2$$\beta $$x + $$\gamma $$ = 0 and x² + x – 1 = 0 have a common root, then $$\alpha $$($$\beta $$ + $$\gamma $$) is equal to :

The number of real roots of the equation
5 + |2^x – 1| = 2^x (2^x – 2) is