Question

Let a and b are roots of \(x^2 – 7x – 1 = 0\). The value of \(\frac{(a_{21} + b_{21} + a_{17} + b_{17})}{(a_{19} + b_{19})}\) is?

• A. 29
• B. 49
• C. 53
• D. 51

Answer 1

The Correct Option is D

The correct answer is option (D) : 51

\(\frac{a^{17}(a^4+1)+b^{17}(b^4+1)}{a^{19}+b^{19}}\)
\(\alpha^2-1=7\alpha\)
\(\Rightarrow \alpha^4+1=51\alpha^2\)\(\large<^{\large{a}}_{\large{b}}\)
\(\therefore \frac{51a^{19}+51b^{19}}{a^{19}+b^{19}}\)

Answer 2

The correct answer is the option (D) 51