If \[\alpha ,\beta \] be the roots of the equation \[{{x}^{2}}-px+q=0\] and \[{{\alpha }_{1}},\,\,{{\beta }_{1}}\] the roots of the equation \[{{x}^{2}}-qx+p=0,\] then the equation whose roots are \[\frac{1}{{{\alpha }_{1}}\beta }+\frac{1}{\alpha {{\beta }_{1}}}\] and \[\frac{1}{\alpha {{\alpha }_{1}}}+\frac{1}{\beta {{\beta }_{1}}}\] is

• A. \[pq{{x}^{2}}-pqx+{{p}^{2}}+{{q}^{2}}+4pq=0\]
• B. \[{{p}^{2}}{{q}^{2}}{{x}^{2}}-{{p}^{2}}{{q}^{2}}x+{{p}^{3}}+{{q}^{3}}-4pq=0\]
• C. \[{{p}^{3}}{{q}^{3}}{{x}^{2}}-{{p}^{3}}{{q}^{3}}x+{{p}^{4}}+{{q}^{4}}-4{{p}^{2}}{{q}^{2}}=0\]
• D. \[(p+q){{x}^{2}}-(p+q)x+{{p}^{2}}+{{q}^{2}}+pq=0\]