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Question Number 9762 by supungamage001 last updated on 31/Dec/16

If cos^(−1) x_1 +cos^(−1) x_2 +...+cos^(−1) x_n =nπ,  then  x_1  + x_2 ^2  + x_3 ^3  + ...+ x_n ^n  =

$$\mathrm{If}\:\mathrm{cos}^{−\mathrm{1}} {x}_{\mathrm{1}} +\mathrm{cos}^{−\mathrm{1}} {x}_{\mathrm{2}} +...+\mathrm{cos}^{−\mathrm{1}} {x}_{{n}} ={n}\pi, \\ $$$$\mathrm{then}\:\:{x}_{\mathrm{1}} \:+\:{x}_{\mathrm{2}} ^{\mathrm{2}} \:+\:{x}_{\mathrm{3}} ^{\mathrm{3}} \:+\:...+\:{x}_{{n}} ^{{n}} \:= \\ $$

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