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Question Number 113109 by bemath last updated on 11/Sep/20

Commented by bemath last updated on 11/Sep/20

$$\mathrm{any}\mathrm{one}\mathrm{help}\mathrm{this}\mathrm{question}?$$

Commented by bemath last updated on 11/Sep/20

$$\left(1\right)+\left(2\right)+\left(3\right)$$$$2({7\mathrm{x}}^2+{7\mathrm{y}}^2+{7\mathrm{z}}^2+9\mathrm{xy}+9\mathrm{xz}+9\mathrm{yz})+$$$$13(\mathrm{xy}+\mathrm{xz}+\mathrm{yz})+3({\mathrm{x}}^2+{\mathrm{y}}^2+{\mathrm{z}}^2)=14$$$$2(7{(\mathrm{x}+\mathrm{y}+\mathrm{z})}^2-14(\mathrm{xy}+\mathrm{xz}+\mathrm{yz}))+31(\mathrm{xy}+\mathrm{xz}+\mathrm{yz})+$$$$3{(\mathrm{x}+\mathrm{y}+\mathrm{z})}^2-6(\mathrm{xy}+\mathrm{xz}+\mathrm{yz})=14$$

Answered by MJS_new last updated on 11/Sep/20

$$\left(\mathrm{iii}\right)-\left(\mathrm{ii}\right)$$$$4(x-y)z+4(x^2-y^2)=5$$$$\Rightarrow z=-\frac{4x^2-4y^2-5}{4(x-y)}$$$$\{\begin{array}{l}16x^4-16x^{3}y-16{xy}^3+16y^4+44x^2+32xy-76y^2+75=0\\ 16x^4-16x^{3}y-16{xy}^3+16y^4+164x^2+208xy-44y^2+175=0\\ z=-\frac{4x^2-4y^2-5}{4(x-y)}\end{array}$$$$\left(\mathrm{i}\right)-\left(\mathrm{ii}\right)$$$$52x^2-44xy-8y^2-25=0$$$$\mathrm{let}x=u-v\wedge y=u+v$$$$88v^2-120uv-25=0$$$$\Rightarrow u=\frac{88v^2-25}{120v}$$$$\mathrm{insert}\mathrm{in}\left(\mathrm{i}\right)\mathrm{or}\left(\mathrm{ii}\right)$$$$v^4-\frac{25v^2}{14}+\frac{625}{784}=0$$$${(28v^2-25)}^2=0$$$$\Rightarrow v=\pm \frac{5\sqrt{7}}{14}$$$$\Rightarrow u=\pm \frac{5\sqrt{7}}{28}$$$$\Rightarrow (x\mid y\mid z)=\pm (-\frac{5\sqrt{7}}{28}\mid \frac{15\sqrt{7}}{28}\mid -\frac{17\sqrt{7}}{28})$$

Commented by bemath last updated on 11/Sep/20

$$\mathrm{waw}....{\mathrm{i}}^{\prime }\mathrm{m}\mathrm{stuck}\mathrm{sir}$$

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