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JEE Previous Year Question

$Let α, β be roots of x^{2} + 2 x - 8 = 0 . If U_{n} = α^{n} + β^{n}, then \frac{U _{10} + 2 U _{9}}{2 U _{8}} is equal to_______$

Topic: JEE PYQ

Answer: 4. Full step-by-step solution below.

Correct answer: 4

Solution

(4) Sol. \frac{α ^{10} + β ^{10} + 2 ( α ^{9} + β ^{9} )}{2 ( α ^{8} + β ^{8} )} \frac{α ^{8} ( α ^{2} + 2 α ) + β ^{8} ( β ^{2} + 2 β )}{2 ( α ^{8} + β ^{8} )} \frac{8 α ^{8} + 8 β ^{8}}{2 ( α ^{8} + β ^{8} )} = 4

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