# 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 \(a+b\).