
Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion 
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May 9th, 2018, 03:20 AM  #1 
Newbie Joined: Apr 2018 From: Banovo Brdo Posts: 12 Thanks: 0  System of equations
$\begin{aligned} x^2+xy+y^2=1\\ x^2+xz+z^2=4\\ y^2+zy+z^2=7 \end{aligned}$ Subtracting 1st from 2nd, and 2nd from 3rd: $\begin{aligned} &(zy)(x+y+z)=3\\ &(yx)(x+y+z)=3\\ &\implies zy=yx\Leftrightarrow z=2yx \end{aligned}$ How do I proceed from here? I've been at it for quite a while, and I still feel like I'm just short of untangling it. Thanks. 
May 9th, 2018, 03:44 AM  #2 
Member Joined: Jan 2018 From: Belgrade Posts: 55 Thanks: 2 
Try to do this: $\displaystyle (yx) \cdot 3y=3$, that is: $\displaystyle (yx) \cdot y=1$. From here: $\displaystyle x=y\frac{1}{y}$. Put it in the first equation, and you get: $\displaystyle 3y^{2}+\frac{1}{y^{2}}=4$ Substitute $\displaystyle t=y^{2}$ and you have: $\displaystyle 3t^{2}4t+1=0$ 

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