Menu Close

x-1-x-2-x-3-2-x-2-x-4-x-5-x-2-x-2-x-3-x-4-2-x-3-x-5-x-1-x-3-x-3-x-4-x-5-2-x-4-x-1-x-2-x-4-x-4-x-5-x-1-2-x-5-x-2-x-3-x-




Question Number 206074 by MATHEMATICSAM last updated on 06/Apr/24
(x_1  − x_2  + x_3 )^2  = x_2 (x_4  + x_5  − x_2 )  (x_2  − x_3  + x_4 )^2  = x_3 (x_5  + x_1  − x_3 )  (x_3  − x_4  + x_5 )^2  = x_4 (x_1  + x_2  − x_4 )  (x_4  − x_5  + x_1 )^2  = x_5 (x_2  + x_3  − x_5 )  (x_5  − x_1  + x_2 )^2  = x_1 (x_3  + x_4  − x_1 )  Find ((2x_1  + x_2  + x_3 )/(3x_4  − x_5 )) .
$$\left({x}_{\mathrm{1}} \:−\:{x}_{\mathrm{2}} \:+\:{x}_{\mathrm{3}} \right)^{\mathrm{2}} \:=\:{x}_{\mathrm{2}} \left({x}_{\mathrm{4}} \:+\:{x}_{\mathrm{5}} \:−\:{x}_{\mathrm{2}} \right) \\ $$$$\left({x}_{\mathrm{2}} \:−\:{x}_{\mathrm{3}} \:+\:{x}_{\mathrm{4}} \right)^{\mathrm{2}} \:=\:{x}_{\mathrm{3}} \left({x}_{\mathrm{5}} \:+\:{x}_{\mathrm{1}} \:−\:{x}_{\mathrm{3}} \right) \\ $$$$\left({x}_{\mathrm{3}} \:−\:{x}_{\mathrm{4}} \:+\:{x}_{\mathrm{5}} \right)^{\mathrm{2}} \:=\:{x}_{\mathrm{4}} \left({x}_{\mathrm{1}} \:+\:{x}_{\mathrm{2}} \:−\:{x}_{\mathrm{4}} \right) \\ $$$$\left({x}_{\mathrm{4}} \:−\:{x}_{\mathrm{5}} \:+\:{x}_{\mathrm{1}} \right)^{\mathrm{2}} \:=\:{x}_{\mathrm{5}} \left({x}_{\mathrm{2}} \:+\:{x}_{\mathrm{3}} \:−\:{x}_{\mathrm{5}} \right) \\ $$$$\left({x}_{\mathrm{5}} \:−\:{x}_{\mathrm{1}} \:+\:{x}_{\mathrm{2}} \right)^{\mathrm{2}} \:=\:{x}_{\mathrm{1}} \left({x}_{\mathrm{3}} \:+\:{x}_{\mathrm{4}} \:−\:{x}_{\mathrm{1}} \right) \\ $$$$\mathrm{Find}\:\frac{\mathrm{2}{x}_{\mathrm{1}} \:+\:{x}_{\mathrm{2}} \:+\:{x}_{\mathrm{3}} }{\mathrm{3}{x}_{\mathrm{4}} \:−\:{x}_{\mathrm{5}} }\:. \\ $$
Commented by A5T last updated on 06/Apr/24
2. Equality when x_1 =x_2 =x_3 =x_4 =x_5
$$\mathrm{2}.\:{Equality}\:{when}\:{x}_{\mathrm{1}} ={x}_{\mathrm{2}} ={x}_{\mathrm{3}} ={x}_{\mathrm{4}} ={x}_{\mathrm{5}} \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *