Basic Algebra Test P\mathfrak{P}a\mathfrak{a}r\mathfrak{r}t\mathfrak{t}3\mathfrak{3}

Algebra Level 4

Given that a,b,c,x,z,yR\displaystyle a,b,c,x,z,y \in \mathbb{R} and;

a2=by+czb2=cz+axc2=ax+by,\begin{aligned} a^2&=by+cz\\ b^2&=cz+ax\\ c^2&=ax+by, \end{aligned}

find the value of xa+x+yb+y+zc+z3.\displaystyle \dfrac{x}{a+x} +\dfrac{y}{b+y} + \dfrac{z}{c+z} - 3.

Also try Basic Algebra Test Part 2 and Basic Algebra Test
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