Let α , β be roots of x 2 + 2 x − 8 = 0 . If U n = α n + β n , then 2 U 8 U 10 + 2 U 9 is equal to______

2 ( α 8 + β 8 ) α 10 + β 10 + 2 ( α 9 + β 9 ) 2 ( α 8 + β 8 ) α 8 ( α 2 + 2 α ) + β 8 ( β 2 + 2 β ) 2 ( α 8 + β 8 ) 8 α 8 + 8 β 8 = 4

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Mathematics - Quadratic Equation Question with Solution | TestHub

MathematicsQuadratic EquationTheory of equationsMedium2 minPYQ_2024

MathematicsMediumnumerical

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______

Answer:

4.00

Solution:

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

Stream:JEESubject:MathematicsTopic:Quadratic EquationSubtopic:Theory of equations

⏱ 2mℹ️ Source: PYQ_2024

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