# Only real no.s

Algebra Level 5

What is the minimum value of the expression $$2{ x }^{ 2 }+2{ y }^{ 2 }+5{ z }^{ 2 }-2xy-4yz-2x-4z+15$$ where $$x,y$$ and $$z$$ are all real numbers. If the answer can be expressed as $$\frac ab$$ where $$a$$ and $$b$$ are coprime positive integers, write the answer as $$a+b$$.

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