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Question Number 40813 by behi83417@gmail.com last updated on 27/Jul/18

Commented by MrW3 last updated on 28/Jul/18

x=y=z=2

$${x}={y}={z}=\mathrm{2} \\ $$

Commented by MrW3 last updated on 28/Jul/18

⇒x^2 +y^2 =xyz  ⇒y^2 +z^2 =xyz  ⇒z^2 +x^2 =xyz  ⇒x^2 =y^2 =z^2   ⇒∣x∣=∣y∣=∣z∣    if x=−y then z=0 but z≠0  ⇒x=y ⇒z=2  similarly  ⇒y=z ⇒x=2  ⇒z=x ⇒y=2

$$\Rightarrow{x}^{\mathrm{2}} +{y}^{\mathrm{2}} ={xyz} \\ $$$$\Rightarrow{y}^{\mathrm{2}} +{z}^{\mathrm{2}} ={xyz} \\ $$$$\Rightarrow{z}^{\mathrm{2}} +{x}^{\mathrm{2}} ={xyz} \\ $$$$\Rightarrow{x}^{\mathrm{2}} ={y}^{\mathrm{2}} ={z}^{\mathrm{2}} \\ $$$$\Rightarrow\mid{x}\mid=\mid{y}\mid=\mid{z}\mid \\ $$$$ \\ $$$${if}\:{x}=−{y}\:{then}\:{z}=\mathrm{0}\:{but}\:{z}\neq\mathrm{0} \\ $$$$\Rightarrow{x}={y}\:\Rightarrow{z}=\mathrm{2} \\ $$$${similarly} \\ $$$$\Rightarrow{y}={z}\:\Rightarrow{x}=\mathrm{2} \\ $$$$\Rightarrow{z}={x}\:\Rightarrow{y}=\mathrm{2} \\ $$$$ \\ $$

Commented by tanmay.chaudhury50@gmail.com last updated on 28/Jul/18

excellent...

$${excellent}... \\ $$

Commented by behi83417@gmail.com last updated on 28/Jul/18

thank you so much dear master.  Q#40457 still waiting for your attintion  sir.

$${thank}\:{you}\:{so}\:{much}\:{dear}\:{master}. \\ $$$${Q}#\mathrm{40457}\:{still}\:{waiting}\:{for}\:{your}\:{attintion} \\ $$$${sir}. \\ $$

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