question_answer

If \[{{\mathbf{4}}^{\mathbf{x}}}\mathbf{ = }{{\mathbf{2}}^{\mathbf{y}}}\mathbf{ = 1}{{\mathbf{6}}^{\mathbf{z}}}\mathbf{= 256}\], then find the value of \[{{\mathbf{x}}^{\mathbf{2}}}+\text{ }{{\mathbf{y}}^{\mathbf{2}}}+\text{ }{{\mathbf{z}}^{\mathbf{2}}}+\text{ }\mathbf{2xy}\text{ }+\text{ }\mathbf{2yz}\text{ }+\text{ }\mathbf{2zx}.\]

A) 120 

B)  196

C)  186     

D)  190

E)  None of these