Question

escreva as equaçoes na foema geral (organize se ) e resolva a)x²+3=4x b)-20=-x-x² c)4x²+7x+3=2x²+2x d) x(x-2)=2(x+6)

Answer 1

Resposta:

a) x²-4x+3=0

S={3,1}

b) x²+x-20=0

S={4,-5}

c) 2x²+5x+3=0

S= {-1,-3/2}

d)x²+1x-12=0

S={3,-4}

Explicação passo-a-passo:

a)x²+3=4x

x²-4x+3=0

a=1 b= -4 c=3

Utilizando Bhaskara:

∆= (-4)²-4*1*3

∆= 16-12

∆= 4

x= -(-4)±√4/2*1

x= 4±2/2

x¹= 4+2/2 = 6/2 = 3

x²= 4-2/2= 2/2= 1

S={3,1}

b)-20=-x-x²

x²+x-20=0

a= 1 b=1 c= -20

∆= 1²-4*1*(-20)

∆= 1+80

∆= 81

x= -1±√81/2*1

x= -1±9/2

x¹= -1+9/2 = 8/2 = 4

x²= -1-9/2 = -10/2 = -5

S={4,-5}

c)4x²+7x+3=2x²+2x

4x²-2x²+7x-2x+3=0

2x²+5x+3=0

a= 2 b= 5 c= 3

∆= 5²-4*2*3

∆= 25-24

∆=1

x= -5±1/2*2

x= -5±1/4

x¹= -5+1/4 = -4/4 = -1

x²= -5-1/4 = -6/4 = -3/2

S= {-1,-3/2}

d)x(x-2)=2(x+6)

x²-2x=2x+12

x²-2x-2x-12=0

x²+1x-12=0

a=1 b= 1 c= =12

∆= 1²-4*1*(-12)

∆ = 1+48

∆= 49

x= -1±√49/2*1

x= -1±7/2

x¹= -1+7/2 = 6/2 = 3

x²= -1-7/2 = -8/2 = -4

S={3,-4}

Bons estudos! Da a melhor resposta.