Răspuns:
Explicație pas cu pas:
x² + 4x + 2 = 0
a = 1 ; b = 4 ; c = 2
∆ = b² - 4ac = 4² - 4 × 1 × 2 = 16 - 8 = 8
[tex]x_1 = \frac{ - b + \sqrt{ \triangle} }{2a} = \frac{ - 4 + \sqrt{8} }{2} = \frac{ - 4 + 2 \sqrt{2} }{2} = \frac{\not2( - 2 + \sqrt{2}) }{\not2} = - 2 + \sqrt{2} \\ [/tex]
[tex]x_2 = \frac{ - b - \sqrt{ \triangle} }{2a} = \frac{-4-\sqrt{8}}{2} =\frac{ - 4 - 2 \sqrt{2} }{2} = \frac{\not2( - 2 - \sqrt{2} )}{\not2} = - 2 - \sqrt{2} \\ [/tex]
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x1 + x2 + 2 × x1 × x2 = - 2 + √2 + (- 2 - √2) + 2(- 2 + √2)(- 2 - √2)
= - 2 + √2 - 2 - √2 + 2(4 - 2)
= - 2 - 2 + 2 × 2
= - 2 - 2 + 4 = - 4 + 4 = 0
