diketahui persamaan kuadrat 2x² + 6x + 7 =0 mempunyai akar akar x1 dan x2 .nilai dari x1² + x2² adalah

a = 2, b = 6, c = 7
[tex]x1 + x2 = \frac{ - b}{a} = \frac{ - 6}{2} = - 3 \\ x1 \times x2 = \frac{c}{a} = \frac{7}{2} [/tex]
maka
[tex] {x1}^{2} + {x2}^{2} \\ = {(x1 + x1)}^{2} - 2x1x2 \\ = {( - 3)}^{2} - 2. \frac{7}{2} [/tex]
2 dg 2 dicoret

sisanya
[tex] = 9 - 7 = 2[/tex]

[tex]2 {x }^{2} + 6x + 7 = 0[/tex]

[tex] {x}^{2} + 6x + 9 + {x}^{2} - 2 = 0[/tex]
[tex] {(x + 3)}^{2} - \sqrt{ {(2 - {x}^{2}) }^{2} } = 0[/tex]
[tex](x + 3 + \sqrt{2 - {x}^{2} } )(x + 3 - \sqrt{2 - {x}^{2} } )[/tex]
ut x1
[tex]x + 3 = - \sqrt{2 - {x}^{2} } \\ {(x + 3)}^{2} = {x}^{2} - 2 \\ {x}^{2} + 6x + 9 = {x}^{2} - 2 \\ 6x = - 11 \\ x = - \frac{11}{6} [/tex]
ut x2
[tex]x + 3 = \sqrt{2 - {x}^{2} } \\ {(x + 3)}^{2} = 2 - {x}^{2} \\ {x}^{2} + 6x + 9 = 2 - {x}^{2} \\ 2 {x}^{2} + 6x + 7 = 0[/tex]