Theory Of Equations Ques 57
- If $a_4=28$, then $p+2 q=$
14
7
21
12
Show Answer
Answer:
Correct Answer: 57.(d)
Solution:
- $\alpha=\frac{1+\sqrt{5}}{2}, \beta=\frac{1-\sqrt{5}}{2}$
$a _4=a _3+a _2$
$=2 a_2+a_1$
$=3a_1+2a_0$
$28=p(3 \alpha+2)+q(3 \beta+2)$
$ \begin{aligned} & 28=(p+q) (\frac{3}{2}+2)+(p-q) (\frac{3 \sqrt{5}}{2}) \\ & \therefore \quad p-q=0 \\ & \text { and } \quad(p+q) \times \frac{7}{2}=28 \\ & \Rightarrow \quad p+q=8 \\ & \Rightarrow \quad p=q=4 \\ & \therefore \quad p+2 q=12 \end{aligned} $
BETA
