Question

qual é o conjunto solução de:
(x-2)(x+2) - (x-1)² = x² - 8

Answer 1

$(x-2)(x+2)-(x-1)^2=x^2-8 \\ \\ x^2+\not2x-\not2x-4-(x^2-2x+1)=x^2-8 \\ \\ \not x^{2} -4-\not x^2+2x-1-x^2+8=0 \\ \\ -x^2+2x-5+8=0 \\ \\ -x^2+2x+3=0~~~\times(-1) \\ \\ x^{2} -2x-3=0 \\ \\ a=1 \\ b=-2 \\ c=-3 \\ \\ \Delta=b^2-4ac \\ \Delta=(-2)^2-4(1)(-3) \\ \Delta=4+12 \\ \Delta=16 \\ \sqrt{\Delta} = \sqrt{16} \\ \sqrt{\Delta} =4 \\ \\ x= \frac{-b\pm \sqrt{\Delta} }{2a} = \frac{-(-2\pm4}{2} = \frac{2\pm4}{2} \\ \\ x'= \frac{2+4}{2} = \frac{6}{2} =3 \\ \\ x"= \frac{2-4}{2} =- \frac{2}{2} =-1$