JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
If \(a\) and \(b\) are the roots of equation \(x^2-7 x-1=0\), then the value of \(\frac{a^{21}+b^{21}+a^{17}+b^{17}}{a^{19}+b^{19}}\) is equal to \(........\).
- A \(50\)
- B \(51\)
- C \(52\)
- D \(53\)
Answer & Solution
Correct Answer
(B) \(51\)
Step-by-step Solution
Detailed explanation
\(x^2-7 x-1=0 < _b^a\) By newton's theorem \(S _{ n +2}-7 S _{ n +1}- S _{ n }=0\) \(S _{21}-7 S _{20}- S _{19}=0\) \(S _{20}-7 S _{19}- S _{18}=0\) \(S _{19}-7 S _{18}- S _{17}=0\) \(\frac{ S _{21}+ S _{17}}{ S _{19}}=\frac{ S _{21}+\left( S _{19}-7 S _{18}\right)}{ S _{19}}\)…
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