Positive x 1 , x 2 , x 3 , x 4 are roots of x 4 − 4 x 3 + a x 2 − b x + 1 = 0 . Find ∑ i = 1 4 tan − 1 x i .

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MathematicsInverse Trigonometric FunctionsSum And Difference Of AnglesMedium2 minQB

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Positive $x_{1}, x_{2}, x_{3}, x_{4}$ are roots of $x^{4} - 4 x^{3} + a x^{2} - b x + 1 = 0$ . Find $\sum_{i = 1}^{4} tan^{- 1} x_{i}$ .

Answer:

Solution:

Arithmetic and geometric means are both 1, so all roots are 1 and the sum is $π$ .

Stream:JEESubject:MathematicsTopic:Inverse Trigonometric FunctionsSubtopic:Sum And Difference Of Angles

⏱ 2mℹ️ Source: QB

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