Question

1) ENCONTRE O CONJUNTO DE SOLUÇÕES DAS SEGUINTES EQUAÇÕES:

A) X²-4X +3 =0
___________
___________
___________

B) 3X² +2X = 0
___________
___________
___________

C) X² -3X +2 = 0
___________
___________
___________

D) X² -8X +7 = 0
___________
___________
___________

E) 2X²-3 = 0
__________
__________
__________​​

Answer 1

Respostas

A) S = {1,3}

B) S ={$-\frac{2}{3} ,0$}

C) S = {1,2}

D) S = {1,7}

E)S =  $\pm\frac{\sqrt{24} }{4}$

Para resolvermos a sua equação abaixo, precisamos achar os coeficientes (a b e c), calcular delta, e por fim bhaskara.

A) X²-4X +3 =0

Coeficientes     $a=1\\b=-4\\c=3$

Delta

$\Delta=4^{2} -4.1.3$

$\Delta=16-4.1.3$

$\Delta=16-12$

$\Delta=4$

bhaskara

$\frac{x=-b\pm\sqrt{\Delta} }{2a}$

Substituindo os valor ( a b e c) na formula de delta.

$\frac{x=-(4)\pm\sqrt{4} }{2}$

$\frac{x=4\pm2}{2}$

$x1=\frac{4+2}{2} =6/2=3$

$x2=\frac{4-2}{2} =2\div 2=1$

S = {1,3}

B) 3X² +2X = 0

Coeficientes    $A=3\\B=2\\C=0$

Delta

$\Delta=2^{2} -4.3.0$

$\Delta=4-4.3.0$

$\Delta=4-0$

$\Delta=4$

Bhaskara

$\frac{x=-b\pm\sqrt{\Delta} }{2a}$

Substituindo os valor ( a b e c) na formula de delta.

$\frac{x=-(+2)\pm\sqrt{4} }{6}$

$\frac{x=-2\pm2}{6}$

$x1=\frac{x=-2+2}{6} =0\div6=0$

$x2=\frac{-2-2}{6} =-\frac{4}{6} \div2=-\frac{2}{3}$

S = (-2/3,0)

C) X² -3X +2 = 0

coeficientes  $A=1\\B=-3\\C=2$

Delta

$\Delta=3^{2} -4.1.2$

$\Delta=9-4.1.2$

$\Delta=9-8$

$\Delta=1$

bhaskara

$\frac{x=-b\pm\sqrt{\Delta} }{2a}$

Substituindo os valor ( a b e c) na formula de delta.

$\frac{x=-(-3)\pm\sqrt{1} }{2}$

$\frac{x=3\pm1}{2}$

$x1=\frac{3+1}{2} =4\div2=2$

$x2=\frac{3-1}{2} =2\div2=1$

S = {1,2}

D) X² -8X +7 = 0

coeficientes    $a=1\\b=-8\\c=7$

Delta

$\Delta=8^{2} -4.1.7$

$\Delta=64-4.1.7$

$\Delta=64-28$

$\Delta=36$

bhaskara

$\frac{x=-b\pm\sqrt{\Delta} }{2a}$

Substituindo os valor ( a b e c) na formula de delta.

$\frac{x=-(-8)\pm\sqrt{36} }{2}$

$\frac{x=8\pm6}{2}$

$x1=\frac{8+6}{2} =14\div2=7$

$x2=\frac{8-6}{2} =2\div2=1$

S = {1,7}

E) 2X²-3 = 0

coeficientes    $a=2\\b=0\\c=-3$

Delta

$\Delta=0^{2} -4.2.(-3)$

$\Delta=0-4.2.(-3)$

$\Delta=0+24$

$\Delta=24$

bhaskara

$\frac{x=-b\pm\sqrt{\Delta} }{2a}$

Substituindo os valor ( a b e c) na formula de delta.

$\frac{x=0\pm\sqrt{24} }{2}$

$x1=\frac{0+2\sqrt{24} }{4}=\frac{\sqrt{24} }{4}$

$x2=\frac{x=0-2\sqrt{24} }{4} =-\frac{\sqrt{24} }{4}$

S ={ $\pm\frac{\sqrt{24} }{4}$}