Question

qual a diferença entre o maior e o menor valor de X da equação
$x {}^{2} - \times - 1 =$
a)
$\sqrt{5}$
b)
$\sqrt{2}$
c)
$\sqrt{1}$
d)
$\sqrt{6}$
pfvr com o cálculo
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Answer 1

$\displaystyle \text x^2-\text x-1= 0 \\\\ \text x =\frac{-(-1)\pm\sqrt{(-1)^2-4(-1)}}{2} \\\\\\ \text x = \frac{1\pm\sqrt{1+4}}{2} \to \text x =\frac{1\pm\sqrt{5}}{2} \\\\\\ \text{x}_1=\frac{1+\sqrt{5}}{2} \ \ ; \ \ \text x_2 =\frac{1-\sqrt{5}}{2} \\\\\\ \underline{\text{Diferen{\c c}a entre o maior x e o menor x}}: \\\\\\ \text x_1-\text x_2 = \frac{1+\sqrt{5}}{2}-\frac{(1-\sqrt{5})}{2} \\\\ \text x_1-\text x_2=\frac{1+\sqrt{5}-1+\sqrt{5}}{2} \\\\ \text x_1-\text x_2=\frac{2\sqrt{5}}{2}$

$\huge\boxed{\ \text x_1-\text x_2=\sqrt 5 \ }\checkmark$

letra a