Explicație pas cu pas:
[tex]{x}^{2} - (m + 1) \cdot x + 2m = 0[/tex]
[tex]S = x_{1} + x_{2} \iff S = m + 1[/tex]
[tex]P = x_{1} \cdot x_{2} \iff P = 2m[/tex]
[tex]3 \cdot ( {x}^{2} _{1} + {x}^{2} _{2}) = x_{1} \cdot x_{2} - 2 \\ 3 \cdot ( {x}^{2} _{1} + {x}^{2} _{2} + 2x_{1}x_{2} - 2x_{1}x_{2}) = x_{1} \cdot x_{2} - 2 \\ [/tex]
[tex]3 \cdot ( {S}^{2} - 2P) = P - 2 \\ 3{S}^{2} - 7P + 2 = 0 \\ 3{(m + 1)}^{2} - 7 \cdot 2m + 2 = 0 \\ 3 {m}^{2} - 8m + 5 = 0 \\ (3m - 5)(m - 1) = 0[/tex]
[tex]3m - 5 = 0 \implies m = \frac{5}{3} \\ m - 1 = 0 \implies m = 1[/tex]
