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If a, b, c are reals such that $$a+b=4$$ and $$2c^2-ab = 4\sqrt{3}c-10$$, find the numerical values of a, b and c.
Correct Answer: a=2 b=2 c=1.7320508076
Substituting $$b=4-a$$ into the second equation and simplifying gives $$2(c-\sqrt{3})^2+(a-2)^2=0$$. Since this is a sum of two non-negative squares equal to zero, both must individually vanish, giving $$c=\sqrt{3}$$ and $$a=2$$. Then $$b=4-a=2$$.
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