Question

Preciso do cálculo dessas equações

Answer 1

Resposta:

Explicação passo-a-passo:

1.a)

x^2-x-6= 0

a = 1; b = - 1; c = - 6

∆ = b^2-4ac

∆ = (-1)^2 - 4.1.(-6)

∆ = 1+24

∆ = 25

x = [-(-1)+/-√25]/2.1

x = [ 1 +/- 5]/2

x' = (1+5)/2 = 6/2 = 3

x" = (1-5)/2 = - 4/2 = - 2

R.: {3; -2}

b)

2x^2-8x+8 = 0 (:2)

x^2 - 4x + 4 = 0

a= 1; b = - 4; c = 4

∆ = b^2-4ac

∆ = (-4)^2 - 4.1.4

∆ = 16-16

∆= 0

x = [- b +/-√∆]/2a

x = [ -(-4)+/-0]/2.1

x =4/2

x = 2

R.: {2}

C)

4x^2+5x+10=0

a= 4; b = 5; c = 10

∆= b^2-4ac

∆= 5^2 - 4.4.10

∆ = 25 - 16.10

∆ = 25 - 160

∆ = - 135

(∆<0: não há solução para os números reais)

D)

2x^2-6x+3= 0

a = 2; b = - 6; c = 3

∆= b^2-4ac

∆ = (-6)^2 - 4.2.3

∆ = 36 - 8.3

∆ = 36 - 24

∆ = 12

√∆= √12 = √4.√3= 2√3

x = [ - b +/- √∆]/2a

x = [- (-6) +/- 2√3]/2.2

x = [6 +/- 2√3]/4

x = 6/4 +/- 2√3/4= 3/2 +/- √3/2

x' = (3+√3)/2

x" = (3-√3)/2

R.:

x' = (3+√3)/2

x" = (3-√3)/2

E)

6x^2+3x+4= - 8x

6x^2 + 3x+8x+4 = 0

6x^2+11x+4 = 0

a = 6; b = 11; c = 4

∆= b^2 - 4ac

∆ = 11^2 - 4.6.4

∆ = 121 - 24.4

∆ = 121 - 96

∆ = 25

x = [- b +/- √∆]/2a

x = [ - 11 +/- √25]/2.6

x = [ - 11 +/- 5]/12

x' = [-11-5]/12=-16/12(:4)/(:4)= -4/3

x"=[-11+5]/12=-6/12(:6)/(:6)= -1/2

R.:{-4/3; -1/2}

F)

2x^2 - 3x = 6 - 4x

2x^2 - 3x+4x - 6 = 0

2x^2 + x - 6 = 0

a = 2; b = 1; c = - 6

∆= b^2 - 4ac

∆ = 1^2 - 4.1.(-6)

∆ = 1 + 24

∆ = 25

x = [- b +/- √∆]/2a

x = [ - 1 +/- √25]/2.2

x = (-1 +/- 5)/4

x' = (-1-5)/4 = -6/4(:2)/(:2)= -3/2

x" = [-1+5)/4 = 4/4 = 1

R.: { 1; -3/2}

2)

A)

X.(x+2)= 3

x^2 + 2x - 3 = 0

a = 1; b = 2; c = - 3

∆= b^2-4ac

∆= 2^2 - 4.1.(-3)

∆ = 4+12

∆ = 16

x = [ - b +/- √∆]/2a

x = [ -2 +/- √16]/2.1

x = [ - 2 +/- 4]/2

x' = (-2+4)/2 = 2/2 = 1

x" = (-2-4)/2 = -6/2= - 3

R.: {1; -3}

B)

x.(x-5)+10 = 4

x^2 - 5x + 10 - 4 = 0

x^2 - 5x + 6 = 0

a = 1; b = - 5; c = 6

∆= b^2-4ac

∆ = (-5)^2 - 4.1.6

∆= 25-24

∆= 1

x = [ - b +/- √∆]/2a

x = [-(-5) +/- √1]/2.1

x = [5 +/- 1]/2

x' = (5+1)/2 = 6/2 = 3

x" = (5-1)/2 = 4/2 = 2

R.: {3; 2}

C)

2x.(4x-1) = 21

8x^2 - 2x - 21 = 0

a= 8; b = - 2; c = - 21

∆ = b^2 - 4ac

∆ = (-2)^2 - 4.8.(-21)

∆ = 4 + 32.21

∆ = 4 + 672

∆ = 676

√∆ = 26

x = [ - b +/- √∆]/2a

x = [ - (-2)+/- √676]/2.8

x = [ 2 +/- 26]/16

x' = [ 2+26]/16= 28/16(:4)/(:4)= 7/4

x" = [2-26]/16= -24/16(:8)/(:8)= -3/2

R.: {7/4; -3/2}