Question

Resolva as equações:

a)$(x+1)^2=7+x$

b)$(x-2)^2-x=1$

Answer 1

a)  (x + 1)² = 7 + x
     (x + 1) . (x + 1) = 7 + x
      x² + 2x + 1 = 7 + x
      x² + 2x - x = 7 - 1
      x² + x - 6 = 0 - fazer bhaskara

      x = $\frac{-1+- \sqrt{ 1^{2}-4(1)(-6) } }{2(1)}$
      x = $\frac{-1+- \sqrt{25} }{2}$
      x' = $\frac{-1-5}{2} = \frac{-6}{2} = -3$
      x'' = $\frac{-1+5}{2} = \frac{4}{2} = 2$


b)  (x - 2)² - x = 1
     (x - 2) . (x - 2) - x = 1
      x² - 4x + 4 - x = 1
      x² - 5x + 3 = 0
 
      x = $\frac{5+- \sqrt{ -5^{2}-4(1)(3) } }{2(1)}$
      x = $\frac{5+- \sqrt{25-12} }{2}$
      x' = $\frac{5+ \sqrt{13} }{2}$
      x'' = $\frac{5- \sqrt{13} }{2}$