Question

1) Use a fórmula resolutiva e resolva essas equações no conjunto números reais.

g) x2 - 2x - 360 = 0
h) x2 - 7x + 10 = 0​

Answer 1

Explicação passo-a-passo:

h)

${x}^{2} - 2x - 360 = 0$

$x = \frac{ - ( - 2)± \sqrt{ {( - 2)}^{2} - 4 \times 1 \times ( - 360) } }{2 \times 1}$

$x = \frac{ - ( - 2) ±\sqrt{ {( - 2)}^{2} - 4 \times ( - 360)} }{2 \times 1}$

$x = \frac{ - ( - 2)± \sqrt{ {( - 2)}^{2} - 4 \times ( - 360) } }{2}$

$x = \frac{ 2± \sqrt{ {( - 2)}^{2} - 4 \times ( - 360) } }{2}$

$x = \frac{2± \sqrt{4 - 4 \times ( - 360)} }{2}$

$x = \frac{2± \sqrt{4 + 1440} }{2}$

$x = \frac{2± \sqrt{1444} }{2}$

$x = \frac{2±38}{2}$

$x = \frac{2 + 38}{2} \\ x = \frac{2 - 38}{2}$

$x = 20 \\ x = - 18$

$\boxed{ x_{1} = 20} \\ \boxed{ x_{2} = - 18}$

h)

${x}^{2} - 7x + 10 = 0$

$x = \frac{ - ( - 7)± \sqrt{ {( - 7)}^{2} - 4 \times 1 \times 10 } }{2 \times 1}$

$x = \frac{ - ( - 7)± \sqrt{ {( - 7)}^{2} - 4 \times 10} }{2}$

$x = \frac{7± \sqrt{ {( - 7)}^{2} - 4 \times 10} }{2}$

$x = \frac{7± \sqrt{49 - 4 \times 10} }{2}$

$x = \frac{7± \sqrt{49 - 40} }{2}$

$x = \frac{7± \sqrt{9} }{2}$

$x = \frac{7±3}{2}$

$x = \frac{7 + 3}{2} \\ x = \frac{7 - 3}{2}$

$x = 5 \\ x = 2$

$\boxed{ x_{1} = 5} \\ \boxed{ x_{2} = 2 }$

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