Theory of Equations 1 Question 56
57. $a _{12}=$
(a) $a _{11}+2 a _{10}$
(b) $2 a _{11}+a _{10}$
(c) $a _{11}-a _{10}$
(d) $a _{11}+a _{10}$
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Solution:
- $\quad \alpha^{2}=\alpha+1$
$$ \beta^{2}=\beta+1 $$
$$ \begin{aligned} a _n & =p \alpha^{n}+q \beta^{n} \\ & =p\left(\alpha^{n-1}+\alpha^{n-2}\right)+q\left(\beta^{n-1}+\beta^{n-2}\right) \\ & =a _{n-1}+a _{n-2} \\ \therefore \quad a _{12} & =a _{11}+a _{10} \end{aligned} $$
