Let alpha and beta be two real numbers such t | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

$x ^{2}- x -1=0 \quad$ roots $=\alpha, \beta$

$\alpha^{2}-\alpha-1=0 \Rightarrow \alpha^{ n +1}=\alpha^{ n }+\alpha^{ n -1}$

$\beta^{2}-\beta-1=

Vedclass · Accepted Answer

$324$

Vedclass · Answer

$x ^{2}- x -1=0 \quad$ roots $=\alpha, \beta$

$\alpha^{2}-\alpha-1=0 \Rightarrow \alpha^{ n +1}=\alpha^{ n }+\alpha^{ n -1}$

$\beta^{2}-\beta-1=0 \Rightarrow \beta^{ n +1}=\beta^{ n }+\beta^{ n -1}$

$\quad\quad\quad\quad\quad\quad\quad\quad+$_______________________

$\quad\quad\quad\quad\quad\quad\quad\quad P_{n+1}=P_{n}+P_{n-1}$

$\quad\quad\quad\quad\quad\quad\quad\quad 29=P_{n}+11$

$\quad\quad\quad\quad\quad\quad\quad\quad P_{n}=18$

$\quad\quad\quad\quad\quad\quad\quad\quad P_{n}^{2}=324$

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 $n \geq 1 .$ Then, the value of $p _{ n }^{2}$ is .... .

Similar Questions

The solutions of the quadratic equation ${(3|x| - 3)^2} = |x| + 7$ which belongs to the domain of definition of the function $y = \sqrt {x(x - 3)} $ are given by

If $a, b, c, d$ are four distinct numbers chosen from the set $\{1,2,3, \ldots, 9\}$, then the minimum value of $\frac{a}{b}+\frac{c}{d}$ is

The number of real solution(s) of the equation $x^2+3 x+2=\min \{|x-3|,|x+2|\}$ is:

Let $x_1, x_2, \ldots, x_6$ be the roots of the polynomial equation $x^6+2 x^5+4 x^4+8 x^3+16 x^2+32 x+64=0$. Then,

Consider the equation $(1+a+b)^2=3\left(1+a^2+b^{2})\right.$ where $a, b$ are real numbers. Then,