Question

Resolva em R, as seguintes equações:

a) x² - 3√3x + 6 = 0

b) (3x - 1)² + (x - 2)² = 25

c) 2 . (x + 3)² - 5 . (x + 3) + 2 = 0

d) x + 1/x = 3

e) (x - 1) . (x + 3) = 5

Answer 1

a) x²-3√3x+6=0
a=1   b=-3√3   c=6

Δ=(-3√3)²-4(1)(6)
Δ=27-24=3

x'=(3√3+√3)/2 = (4√3)/2 = 2√3

x"=(3√3-√3)/2 = (2√3)/2 = √3

b)(3x-1)²+(x-2)²=25
9x²-6x+1+x²-4x+4-25=0
10x²-10x-20=0
x²-x-2=0
Δ=(-1)²-4(1)(-2)=9

x'=(1+3)/2 =4/2 =2

x"=(1-3)/2=-2/2=-1

c)2 . (x+3)²-5 . (x+3)+2=0
2(x²+6x+9)-5x-15+2=0
2x²+12x+18-5x-15+2=0
2x²-7x+5=0
a=2   b= -7   c= 5

Δ=(-7)²-4(2)(5)= 49-40= 9

x'= (7+3)/4=10/4 =5/2

x"= (7-3)/4=4/4=1

d)x+1/x=3
x+1/x-3=0
(x²-3x+1)/x=0
 x não pode ser 0, então
x²-3x+1=0

Δ=(-3)²-4(1)(1)= 9-4=5

x'= (3+√5)/2

x"=(3-√5)/2


e)(x-1)*(x+3)=5
x²+2x-3-5=0
x²+2x-8=0

Δ= 4-4(1)(-8) = 36

x'= (-2+6)/2 =4/2 =2

x"=(-2-6)/2 = -8/2 = -4

Answer 2

a) x²-3√3x+6=0

a=1   b=-3√3   c=6

Δ=(-3√3)²-4(1)(6)

Δ=27-24=3

x'=(3√3+√3)/2 = (4√3)/2 = 2√3

x"=(3√3-√3)/2 = (2√3)/2 = √3

b)(3x-1)²+(x-2)²=25

9x²-6x+1+x²-4x+4-25=0

10x²-10x-20=0

x²-x-2=0

Δ=(-1)²-4(1)(-2)=9

x'=(1+3)/2 =4/2 =2

x"=(1-3)/2=-2/2=-1

c)2 . (x+3)²-5 . (x+3)+2=0

2(x²+6x+9)-5x-15+2=0

2x²+12x+18-5x-15+2=0

2x²-7x+5=0

a=2   b= -7   c= 5

Δ=(-7)²-4(2)(5)= 49-40= 9

x'= (7+3)/4=10/4 =5/2

x"= (7-3)/4=4/4=1

d)x+1/x=3

x+1/x-3=0

(x²-3x+1)/x=0

x não pode ser 0, então

x²-3x+1=0

Δ=(-3)²-4(1)(1)= 9-4=5

x'= (3+√5)/2

x"=(3-√5)/2

e)(x-1)*(x+3)=5

x²+2x-3-5=0

x²+2x-8=0

Δ= 4-4(1)(-8) = 36

x'= (-2+6)/2 =4/2 =2

x"=(-2-6)/2 = -8/2 = -4

ESPERO TER AJUDADO :)