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Question Number 12763 by tawa last updated on 30/Apr/17

Solve simultaneously  2x + y − z = 8        ........... equation (i)  x^2  − y^2  + 2z^2  = 14       .......... equation (ii)  3x^3  + 4y^3  + z^3  = 195         ........... equation (iii)

$$\mathrm{Solve}\:\mathrm{simultaneously} \\ $$$$\mathrm{2x}\:+\:\mathrm{y}\:−\:\mathrm{z}\:=\:\mathrm{8}\:\:\:\:\:\:\:\:...........\:\mathrm{equation}\:\left(\mathrm{i}\right) \\ $$$$\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{y}^{\mathrm{2}} \:+\:\mathrm{2z}^{\mathrm{2}} \:=\:\mathrm{14}\:\:\:\:\:\:\:..........\:\mathrm{equation}\:\left(\mathrm{ii}\right) \\ $$$$\mathrm{3x}^{\mathrm{3}} \:+\:\mathrm{4y}^{\mathrm{3}} \:+\:\mathrm{z}^{\mathrm{3}} \:=\:\mathrm{195}\:\:\:\:\:\:\:\:\:...........\:\mathrm{equation}\:\left(\mathrm{iii}\right) \\ $$

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