Question

a) x²-5x+6=0 b) x²-8x+12=0 c) x²+2x-8=0 d) x²-8x-8=0 e) 2x²-8x+8=0 f) x²-4x-5=0 g) -x²+x+12=0

Answer 1

Resposta:

a) x²-5x+6=0

a = 1       b = -5       c = 6

$x = \frac{-(b) +- \sqrt{(b)^{2} - 4 * a * c} }{2*a}\\\\x = \frac{-(-5) +- \sqrt{(-5)^{2} - 4 * 1 * 6} }{2*1}\\\\x = \frac{5+-\sqrt{25-24} }{2}\\\\x = \frac{5+-\sqrt{1} }{2}\\\\x = \frac{5+-1}{2}\\\\x' = \frac{5+1}{2}=\frac{6}{2} =3\\\\x'' = \frac{5-1}{2}=\frac{4}{2} =2$

b) x²-8x+12=0

a = 1       b = -8       c = 12

$x = \frac{-(b) +- \sqrt{(b)^{2} - 4 * a * c} }{2*a}\\\\x = \frac{-(-8) +- \sqrt{(-8)^{2} - 4 * 1 * 12} }{2*1}\\\\x = \frac{8+-\sqrt{64-48} }{2}\\\\x = \frac{8+-\sqrt{16} }{2}\\\\x = \frac{8+-4}{2}\\\\x' = \frac{8+4}{2}= \frac{12}{2}=6\\\\x' = \frac{8-4}{2}= \frac{4}{2}=2$

c) x²+2x-8=0

a = 1       b = 2       c = -8

$x = \frac{-(2) +- \sqrt{(2)^{2} - 4 * 1 * -8} }{2*1}\\\\x = \frac{-2+-\sqrt{4+32} }{2}\\\\x = \frac{-2+-\sqrt{36} }{2}\\\\x = \frac{-2+-6}{2}\\\\x' = \frac{-2+6}{2}= \frac{4}{2}=2\\\\x' = \frac{-2-6}{2}= \frac{-8}{2}=-4$

d) x²-8x-8=0

a = 1       b = -8       c = -8

$x = \frac{-(b) +- \sqrt{(b)^{2} - 4 * a * c} }{2*a}\\\\x = \frac{-(-8) +- \sqrt{(-8)^{2} - 4 * 1 * -8} }{2*1}\\\\x = \frac{8+-\sqrt{64+32} }{2}\\\\x = \frac{8+-\sqrt{+96} }{2}\\\\x = \frac{8+-4\sqrt{6}}{2}$

não possui raiz exata

e) 2x²-8x+8=0

a = 1       b = -8       c = 8

$x = \frac{-(b) +- \sqrt{(b)^{2} - 4 * a * c} }{2*a}\\\\x = \frac{-(-8) +- \sqrt{(-8)^{2} - 4 * 1 * 8} }{2*1}\\\\x = \frac{8+-\sqrt{64-32} }{2}\\\\x = \frac{8+-\sqrt{32} }{2}\\\\x = \frac{8+-4\sqrt{2}}{2}$

não possui raiz exata

f) x²-4x-5=0

a = 1       b = -4       c = -5

$x = \frac{-(b) +- \sqrt{(b)^{2} - 4 * a * c} }{2*a}\\\\x = \frac{-(-4) +- \sqrt{(-4)^{2} - 4 * 1 * -5} }{2*1}\\\\x = \frac{4+-\sqrt{16+20} }{2}\\\\x = \frac{4+-\sqrt{36} }{2}\\\\x = \frac{4+-6}{2}\\\\x' = \frac{4+6}{2}= \frac{10}{2}=5\\\\x' = \frac{4-6}{2}= \frac{-2}{2}=-1$

g) -x²+x+12=0

a = -1       b = 1       c = 12

$x = \frac{-(b) +- \sqrt{(b)^{2} - 4 * a * c} }{2*a}\\\\x = \frac{-(1) +- \sqrt{(1)^{2} - 4 * -1 * 12} }{2*-1}\\\\x = \frac{-1+-\sqrt{1+48} }{-2}\\\\x = \frac{-1+-\sqrt{49} }{-2}\\\\x = \frac{-1+-7}{-2}\\\\x' = \frac{-1+7}{-2}= \frac{6}{-2}=-3\\\\x' = \frac{-1-7}{-2}= \frac{-8}{-2}=4$