Resolva, em R, as equações a seguir:
Soluções para a tarefa
Resposta:Segue as contas baixo na explicação
Explicação passo-a-passo:
b)x-2/x=1-x/x-1
x-2/x=x-1+x/x-1
x-2/x=2x-1/x-1
(x-2).(x-1)=x.(2x-1)
x²-x-2x+2=2x²-x
x²-3x+2=2x²-x
x²-3x+2-2x²+x=0
-x²-3x+2=0(-1)
x²+3x-2=0
Δ=b²-4.a.c
Δ=3²-4.1.(-2)
Δ=9+8
Δ=17
x=-b ± √Δ/2.a
x=-3 ± √17/2
S(-3+√17/2,-3-√17/2)
c) 9-x/2+4/x-2=3(x-1)/2
9-x/2+4/x-2=3x-3/2
9-x/2+4/x-2=3x-3/2
(9-x).(x-2)/2x-4+2.4/2x-4=3x-3/2
9x-18-x²-2x/2x-4+8/2x-4=3x-3/2
7x-10-x²/2x-4=3x-3/2
2.(7x-10-x²)=(2x-4).(3x-3)
14x-20-2x²=6x²-8x-12x+12
14x-20-2x²=6x²-20x+12
14x-20-2x²-6x²+20x-12=0
-8x²+34x-32=0(-1)
8x²-34x+32=0
Δ=b²-4.a.c
Δ=(-34)²-4.8.32
Δ=1156-1024
Δ=132
x=-b ± √Δ/2.a
x=-(-34) ± √132/2.8
x=34 ± 2√33/16 :2/2
x=17 ± 1√33/8
S(17+1√33/8,17-1√33/8)
d)8/x+1- x/x-1=2/(x+1).(x-1)
8.(x-1)-x(x+1)/(x-1).(x+1)=2/(x+1).(x-1)
8x-8-x²-x/x²-x+x-1=2/x²-x+x-1
8x-8-x²-x=2
7x-8-x²=2
7x-8-x²-2=0
7x-10-x²=0
-x²+7x-10=0(-1)
x²-7x+10=0
Δ=b²-4.a.c
Δ=(-7)²-4.1.10
Δ=49-40
Δ=9
x=-b ± √Δ/2.a
x=-(-7) ± √9/2.1
x=7 ± 3/2
x1=7+3/2
x1=10/2
x1=5
x2=7-3/2
x2=4/2
x2=2
S(5,2)