Logs, Equations and Inequalities

Paragraph 2^{2} – x – 1 = 0, where α ≠ β. For n = 0, 1, 2,...., let a_{n} = pα^{n} + qβ^{n}.FACT : If a and b are rational numbers and $\mathrm{a}+\mathrm{b}\sqrt{5}=0$, then a = 0 = b. |

_{4}= 28, then p + 2q =

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JEE Advanced 2017

Paragraph 2^{2} – x – 1 = 0, where α ≠ β. For n = 0, 1, 2,...., let a_{n} = pα^{n} + qβ^{n}.FACT : If a and b are rational numbers and $\mathrm{a}+\mathrm{b}\sqrt{5}=0$, then a = 0 = b. |

_{12}=

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JEE Advanced 2017