Verified answer

[tex]x {}^{2} - 4x + 2 = 0 \\ x_{1} + x_{2} = 4\\ x_{1} \times x_{2} = 2 \\ x {}^{2} _{1} +x {}^{2} _{2} = x {}^{2} _{1} +2x_{1}x_{2} + x {}^{2} _{2} - 2x_{1}x_{2} \\ (x _{1} +x _{2}) {}^{2} - 2x_{1}x_{2 } \\ \frac{2}{x {}^{2} _{1}} + \frac{2}{x {}^{2} _{2}} = \frac{2(x {}^{2} _{1} +x {}^{2} _{2}) }{(x _{1} \times x _{2}) {}^{2} } = \\ \frac{2((x _{1} +x _{2}) {}^{2} - 2x_{1}x_{2 } )}{(x_{1} \times x_{2}) {}^{2} } = \\ \frac{2( {4}^{2} - 2 \times 2)}{ {2}^{2} } = \\ \frac{16 - 4}{2} = \frac{12}{2} = 6[/tex]