Question

(50 pe 2=100 pe x) (66-x²+x=10)​

Answer 1

Răspuns:

Explicație pas cu pas:

$\frac{50}{2} = \frac{100}{x} \rightarrow x = \frac{2 \times 100}{50} = \frac{200}{50} = 4$

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66 - x² + x = 10

66 - x² + x - 10 = 0

56 - x² + x = 0

x² - x - 56 = 0

a = 1 ; b = - 1 ; c = - 56

∆ = b² - 4ac = 1² - 4 × 1 × (- 56) = 1 - (- 224)

∆ = 1 + 224 = 225 > 0 → ∃ x1 , x2 ∈ ℝ ; x1 ≠ x2

$x_1 = \frac{ - b + \sqrt{ \triangle} }{2a} = \frac{1 + \sqrt{225} }{2} = \frac{1 + 15}{2} = \frac{16}{2} = 8$

$x_2 = \frac{ - b - \sqrt{ \triangle} }{2a} = \frac{1 - \sqrt{225} }{2} = \frac{1 - 15}{2} = \frac{ - 14}{2} = - 7$