Question

me ajudem. tenho 5 questoes, quem responder as 5 , ganha os 16 pontos.
com calculo,por favor 
a) 2x²+4x-6=3x
b) 2x²-3x=2x-1
c) 5x²-x+1=x+4x²
d) x²-2x+3=-12+6x
e) 4x²+7x+3=2x²+2x

Answer 1

a) 2x²+4x-6=3x
2x² +4x -3x -6=0
2x² +x -6=0

a= 2      b= +1      c= -6
▲= b² -4.a.c = (1)² -4.(2).(-6)= 1 +48= 49

x= (-b ± √▲)/2.a
x= [-(+1) ± √49]/2.2
x=[-1 ± 7]/4
x'=[-1 +7]/4= +6/4    simplificando 6 e 4 por 2 = 3/2
x"=[-1-7]/4= -8/4= -2

S{3/2 ; -2}


b) 2x²-3x=2x-1
2x² -3x -2x +1= 0
2x² -5x +1=0

a= 2       b= -5       c= +1
▲= b² -4.a.c = (-5)² -4.(2).(+1)= 25 -8 = 17

x= (-b ± √▲)/2.a
x=[-(-5) ± √17]2.2
x=[+5 ± √17]/4
x'=[5 +√17]/4
x"=[5 - √17]/4

S={ [5 +√17]/4 e [5 - √17]/4}



c) 5x²-x+1=x+4x²
5x² -4x² -x -x +1=0
x² -2x +1=0

a= 1    b= -2     c= +1
▲= b² -4.a.c = (-2)² -4.(1).(+1)= +4 -4 = 0

x= (-b ± √▲)/2.a
x= [-(-2)  ± √0]/2.1
x=[+2  ± 0]/2
x'=[2+0]/2= 2/2= 1
x"=[2-0]/2= 2/2= 1

S{1}


d) x²-2x+3=-12+6x
x² -2x -6x +3 +12=0
x² -8x +15=0

a= 1          b= -8         c= +15

▲= b² -4.a.c = (-8)² -4.(1).(+15)= +64 -60= 4

x= (-b ± √▲)/2.a
x=[-(-8) ± √4]/2.1
x=[+8 ± 2]/2
x'=[8+2]/2= 10/2= 5
x"=[8-2]/2= 6/2= 3

S{5 ; 3}


e) 4x²+7x+3=2x²+2x
4x² -2x² +7x -2x +3=0
2x² +5x +3=0

a= 2       b= +5        c= +3
▲= b² -4.a.c = (5)² -4.(2).(+3)= 25 - 24= 1

x= (-b ± √▲)/2.a
x=[-(+5  ± √1]/2.2
x=[-5  ± 1]/4
x'=[-5 +1]/4= -4/4 = -1
x"=[-5 -1]/4= -6/4       simplificando -6 e 4 por 2 = -3/2

S{-1 ; -3/2}

Answer 2

a. 2x² +4x - 6 = 3x
2x² + 4x - 3x - 6 = 0
2x² + x - 6 = 0 
delta = b² - 4ac
delta = (1)² - 4*2*(-6)
delta = 1 + 48 = 49
x = -1 +/- raiz de 49/2*a
x = -1+/- 7 / 4
x' = -1+7/4= 6/4=3/2
x" = - 1 -7/4 = -8/4 = -2 

b. 2x² - 3x= 2x - 1
2x² - 3x - 2x + 1 = 0
2x² -5x + 1 = 0
delta = (-5)² - 4*2*1
delta = 25 - 8 = 17 não existe raiz de 17

c. 5x² - x + 1 = x + 4x²
5x² - 4x² - x - x + 1 
x² - 2x + 1=0
delta = 2² - 4*1*1
delta = 4 - 4= 0
x = -2 +/- 0 / 2
x'= -2+0/2
x'= -2/2=-1
x"= -2-0/2
x"= -2/2=-1 raízes iguais

d. x² -2x + 3 = 12 + 6x
x² - 2x - 6x = 12-3
x² -8x - 9=0
delta = (-8)² - 4*1*(-9)
delta = 64+36=100
x = -(-8)+/- raiz de 100=10/2
x' = 8+10/2=18/2=9
x"= 8-10/2=-2/2=-1

e. 4x² + 7x + 3 = 2x² + 2x
4x² - 2x² +7x - 2x + 3=0
2x² +5x + 3 =0
delta = 5² - 4*2*3
delta = 25-24=1
x= -5+/-1/4
x' = -5+1/4=-4/4=-1
x" = -5-1/4=-6/4=-3/2