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Question Number 94297 by peter frank last updated on 17/May/20

Commented by mathmax by abdo last updated on 18/May/20

$$weknowthat{x}^2+y^2+z^2=0\Rightarrow x=y=z(forx,y,zreals)$$$$so\left(e\right)\Rightarrow cosx=cos\left(2x\right)=cos\left(3x\right)=0$$$$cosx=0\Rightarrow x=\frac{\pi }{2}+k\pi \to set{w}_{1k}$$$$cos\left(2x\right)=0\Rightarrow x=\frac{\pi }{4}+\frac{k\pi }{2}\to set{w}_{2k}$$$$cos\left(3x\right)=0\Rightarrow x=\frac{\pi }{6}+\frac{k\pi }{3}\to w_{3k}$$$$\Rightarrow x\in \cap w_k(k\in Z)but\frac{\pi }{2}+k\pi =\frac{\pi }{4}+k^{{}^{\prime }}\pi \Rightarrow \frac{1}{2}+k=\frac{1}{4}+k^{{}^{\prime }}\Rightarrow$$$$2+4k=1+4k^{{}^{\prime }}\Rightarrow 1=4(k^{{}^{\prime }}-k)\Rightarrow \mid k-k^{{}^{\prime }}\mid =\frac{1}{4}\to impossible$$$$\Rightarrow xdontexistsomethingwentwrongintheQ...!$$

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