Školjka

%V0 $a^2 = x^2 + y^2 + z^2 + 2xy + 2xz + 2yz = b^2 + 2xy + 2xz + 2yz$ $xy+yz+zx = \frac{a^2-b^2}{2}$ $\frac{a^2-b^2}{2} = xyz \cdot (x^{-1} + y^{-1} + z^{-1}) = xyz \cdot c^{-1}$ $xyz = \frac{a^2c - b^2c}{2}$ $x^3+y^3+z^3 =$ $= (x^3 + y^3 + z^3 - 3xyz) + 3xyz = $ $= (x+y+z)(x^2+y^2+z^2 - xy-xz-yz) + 3xyz=$ $=a(b^2-\frac{a^2-b^2}{2})+3 \frac{a^2c - b^2c}{2}$