Question

© = Resolva as equações abaixo considerando U = R.
a) x2 - 7x + 10 = 0
b) x2 - 49 = 0
c) x2 - 5x = 0
d) x2 + 8x + 15 = 0
e) 6x2 + 5x + 1 = 0​

Answer 1

Explicação passo-a-passo:

$a) {x}^{2} - 7x + 10 = 0 \\ x = \frac{ - ( - 7) + - \sqrt{ {( - 7)}^{2} - 4 \times 1 \times 10} }{2 \times 1} \\ \\ x = \frac{7 + - \sqrt{49 - 40} }{2} \\ \\ x = \frac{7 + - \sqrt{9} }{2} \\ \\ x1 = \frac{7 + 3}{2} = \frac{10}{2} = 5 \\ \\ x2 = \frac{7 - 3}{2} = \frac{4}{2} = 2$

$b) {x}^{2} - 49 = 0 \\ {x}^{2} = 49 \\ x = \sqrt{49 } \\ x1 = 7 \\ x2 = - 7$

$c) {x}^{2} - 5x = 0 \\ x(x - 5) = 0 \\ x1 = 5 \\ x2 = 0$

$d) {x}^{2} + 8x + 15 = 0 \\ x = \frac{ - 8 + - \sqrt{ {8}^{2} - 4 \times 1 \times 15 } }{2 \times 1} \\ \\ x = \frac{ - 8 + - \sqrt{64 - 60} }{2} \\ \\ x = \frac{ - 8 + - \sqrt{4} }{2} \\ \\ x1 = \frac{ - 8 + 2}{2} = \frac{ - 6}{2} = - 3 \\ \\ x2 = \frac{ - 8 - 2}{2} = \frac{ - 10}{2} = - 5$

$e)6 {x}^{2} + 5x + 1 = 0 \\ x = \frac{ - 5 + - \sqrt{ {5}^{2} - 4 \times 6 \times 1} }{2 \times 6} \\ \\ x = \frac{ - 5 + - \sqrt{25 - 24} }{12} \\ \\ x = \frac{ - 5 + - \sqrt{1} }{12} \\ \\ x1 = \frac{ - 5 + 1}{12} = \frac{ - 4}{12} = - \frac{1}{3} \\ \\ x2 = \frac{ - 5 - 1}{12} = \frac{ - 6}{12} = - \frac{1}{2}$