Question

4.Encontre as raízes da equação: (x−5)^2−2x = 3⋅(x−10)−1 * 8 e 7 20 e 14 12 e 10 4 e 2 ​

Answer 1

Oie, tudo bom?

Resposta: 8 e 7.

$(x - 5) {}^{2} - 2x = 3(x - 10) - 1 \\ x {}^{2} - 10x + 25 - 2x = 3x - 30 - 1 \\ x {}^{2} - 12x + 25 = 3x - 31 \\ x {}^{2} - 12x + 25 - 3x + 31 = 0 \\ x {}^{2} - 15x + 56 = 0$

$\boxed{a = 1 \: ,\: b = - 15 \:, \: c = 56}$

$x = \frac{ - b± \sqrt{b {}^{2} - 4ac} }{2a} \\ x = \frac{ - ( - 15)± \sqrt{( - 15) {}^{2} - 4 \: . \: 1 \: . \: 56 } }{2 \: . \: 1} \\ x = \frac{15± \sqrt{225 - 224} }{2} \\ x = \frac{15± \sqrt{1} }{2} \\ x = \frac{15±1}{2} \\ x = \frac{15 + 1}{2} = \frac{16}{2} = \boxed{8} \\ x = \frac{15 - 1}{2} = \frac{14}{2} = \boxed{7}$

$\boxed{S = \left \{ 8 \: , \:7 \right \}}$

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