# Think algebra would be easy?

Geometry Level 5

$$\boxed{\large\text{Challenge}~\sim~\normalsize\text{solve using pure Geometry only!}}$$

In the given $$\bigtriangleup ABC$$, $$AB = 4$$, $$AC = 7$$ and $$\widehat{A} = 60^{\circ}$$, and if $$x_1,~x_2$$ and $$x_3$$ are roots of the equation

$$x^3 - (4R + r)x^2 + s^2x - s^2r = 0$$

where $$R$$ is the circum-radius, $$r$$ is the in-radius and $$s$$ is the semi perimeter of $$\bigtriangleup\!\!\mathrm{ABC}$$. Find the value of $$x_1^3 + x_2^3 + x_3^3$$ rounded to nearest thousandths.

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