Let and be two real numbers such that and

MATHEMATICS · Subjective · CBSE · Mathematics · Polynomials · Polynomials

Problem

Let

\alpha

and

\beta

be two real numbers such that

\alpha + \beta = 1

and

\alpha\beta = -1

. Let

p_n = (\alpha)^n + (\beta)^n

P_{n-1} = 11

and

p_{n+1} = 29

for some integer

n \ge 1

. Then, the value of

p_n^2

is \_\_\_\_.