Question

Resolva, em R, as seguintes equações:
d) x + 1/x=3
e) (x - 1)(x + 3) = 5​

Answer 1

a)

$x + \frac{1}{x} = 3 \\ {x}^{2} + 1 = 3 \\ {x}^{2} = 3 - 1 \\ {x}^{2} = 2 \\ {x} = + - \sqrt{2}$

b)

$(x - 1)(x + 3) = 5 \\ {x}^{2} + 3x - x - 3 = 5 \\ {x}^{2} + 2x - 3 - 5 = 0 \\ {x}^{2} + 2x - 8 = 0 \\ \\ d = 2^{2} - 4 \times 1 \times - 8 \\ d = 4 + 32 \\ d = 36 \\ \\ x1 = \frac{ - 2 + \sqrt{36} }{2 \times 1} \\ x1 = \frac{ - 2 + 6}{2} \\ x1 = \frac{4}{2} \\ x1 = 2 \\ \\ x2 = \frac{ - 2 - 6}{ 2} \\ x2 = \frac{ - 8}{2} \\ x2 = - 4$