Question

Gente me ajudem a maioria eu conseguir fazer só alguns que não
Resolva as equações:
E) -25+100x²=0
F) x²-81/4=0 Obs: esse é 84 em cima e 4 em baixo
G) x²+3x+2=0
I) 6x²+x-1=0
K) -x²+13x-40=0
L) x²-6x+8=0
M) (x-2) - (x-3)=0

Answer 1

$e)\\ \\ 100x^{2} -25=0\\ \\ 100x^{2} =25\\ \\ x^{2} =\frac{25}{100} \\ \\ x=\sqrt{\frac{25}{100}} \\ \\ x=\frac{5}{10} =\frac{1}{2}$

$f)\\ \\ x^{2} -\frac{81}{4} =0\\ \\ x^{2} =\frac{81}{4} \\ \\ x=\sqrt{\frac{81}{4}} \\ \\ x=\frac{9}{2}$

$g)\\ \\ x^{2} +3x+2=0$

Δ = b² - 4.a.c

Δ = 9 - 4.1.2

Δ = 9-8

Δ = 1

$x=\frac{-b+-\sqrt{delta}}{2.a} \\ \\ x=\frac{-3+-\sqrt{1}}{2} \\ \\ x=\frac{-3+-1}{2} \\ \\ x'=\frac{-3+1}{2} =-1\\ \\ x''=\frac{-3-1}{2} =\frac{-4}{2} =-2$

$i)\\ \\ 6x^{2} +x-1=0$

Δ = b² - 4.a.c

Δ = 1² - 4.6.(-1)

Δ = 1 - (-24)

Δ = 1 + 24

Δ = 25

$x=\frac{-b+-\sqrt{delta}}{2.a} \\ \\ x=\frac{-1+-\sqrt{25}}{2.6} \\ \\ x=\frac{-1+-5}{12} \\ \\ x'=\frac{-1+5}{12}=\frac{4}{12} =\frac{1}{3} \\ \\ x''=\frac{-1-5}{12} =-\frac{6}{12} =-\frac{1}{2}$

$k)\\ \\ -x^{2} +13x-40=0$

Δ = b² - 4.a.c

Δ = 13² - 4.(-1).(-40)

Δ = 169 - 160

Δ = 9

$x=\frac{-b+-\sqrt{delta}}{2.a} \\ \\ x=\frac{-13+-\sqrt{9}}{-2} \\ \\ x=\frac{-13+-3}{-2} \\ \\ x'=\frac{-13+3}{-2} =\frac{-10}{-2} =+5\\ \\ x''=\frac{-13-3}{-2} =\frac{-16}{-2} =+8$

$l)\\ \\ x^{2} -6x+8=0$

Δ = b² - 4.a.c

Δ = 36 - 4.1.8

Δ = 36 - 32

Δ = 4

$x=\frac{-b+-\sqrt{delta}}{2.a} \\ \\ x=\frac{6+-\sqrt{4}}{2} \\ \\ x=\frac{6+-2}{2} \\ \\ x'=\frac{6+2}{2} =\frac{8}{2} =4\\ \\ x''=\frac{6-2}{2} =\frac{4}{2} =2$

$m)\\ \\ (x-2)-(x-3)=x-2-x+3=x-x+3-2=1$