Question

Resolva as seguintes equaçoes:

a) (x + 1)² - x = 7 + x
b) (x - 2)² - x = 1
c) x² = $\frac{4}{5}$x + $\frac{1}{5}$
d) $\frac{ x^{2}}{4} - \frac{x}{3} + \frac{1}{9} = 0$
e) x² - 3 = $\frac{x - 3}{6}$
f) $\frac{ x^{2} - 5x}{6} +1 = \frac{2x+11}{3}$

Answer 1

a)$x^{2} +2x+1-x=7+x \\ x^{2} -6=0$
Δ=24
$x=+-\frac{ \sqrt{24} }{2} \\ x^{l} = 2,45 \\ x^{ll} =-2,45$

b)$x^{2} -4x+4-x=1 \\ x^{2} -5x+3=0$
Δ=13
$x= \frac{5+-3,61}{2} \\ x^{l}=4,305 \\ x^{ll} =0,695$

c)$x^{2} =0,8x+0,2 \\ x^{2} -0,8x-0,2=0$
Δ=1,44
$x= \frac{0,8+- \sqrt{1,44} }{2} \\ x^{l} = \frac{2}{2}=1 \\ x^{ll}= \frac{-0,4}{2} =-0,2$

d)$\frac{27 x^{2} }{108} - \frac{36x}{108} + \frac{12}{108} = \frac{0}{108} \\ 27 x^{2} -36x+12=0 \\ 9 x^{2} -12x+4=0$
Δ=0
$x= \frac{12}{18} \\ x= \frac{1}{3}$

e)$6 x^{2} -18=x-3 \\ 6 x^{2} -x-21=0$
Δ=505
$x= \frac{1+-22,48}{12} \\ x^{l} =1,9566... \\ x^{ll} =-1,79$

f)$\frac{ x^{2} -5x}{6} + \frac{6}{6} = \frac{2(2x+11)}{6} \\ x^{2} -5x+6=4x+22 \\ x^{2} -9x-16=0$
Δ=15
$x= \frac{9+-3,87}{2} \\ x^{l} =6,435 \\ x^{ll} =2,565$