Question

Escreva As equações abaixo na forma geral e resolva em R:

a) x(x+3)-40=0
b)10+x(x-2)=2
c)4+x(x-4)=x
d) x(x+5)-2x=28
e) 2x(x+3)= x²+ 3x+10

Answer 1

a) x(x+3)-40=0
x^2+3x-40=0
delta=b^2-4ac
delta=3^2-4.1.(-40)
delta=9+160
delta=169
x=-b-/+ raiz de delta/2a
x=-3-13/2.1
x=-16/2
x=-8
x=-3+13/2.1
x=10/2
x=5
b) 10+x(x-2)=2
10+x^2-2x=2
x^2-2x+10-2
x^2-2x+8=0
delta=b^2-4ac
delta=(-2)^2-4.1.8
delta=4-32
delta=-28
delta negativo não há raízes reais.
c) 4+x(x-4)=x
4+x^2-4x=x
x^2-4x-x+4
x^2-5x+4=0
delta=b^2-4ac
delta=(-5)^2-4.1.4
delta=25-16
delta=9
x=-b-/+ raiz de delta/2a
x=-(-5)-3/2.1
x=5-3/2
x=2/2
x=1
x=-(-5)+3/2.1
x=5+3/2
x=8/2
x=4
d) x(x+5)-2x=28
x^2+5x-2x=28
x^2+3x=28
x^2+3x-28=0
delta=b^2-4ac
delta=3^2-4.1.(-28)
delta=9+112
delta=121
x=-b-/+ raiz de delta/2a
x=-3-11/2.1
x=-14/2
x=-7
x=-3+11/2.1
x=8/2
x=4
e) 2x(x+3)=x^2+3x+10
2x^2+6x=x^2+3x+10
2x^2-x^2+6x-3x=10
x^2+3x=10
x^2+3x-10=0
delta=b^2-4ac
delta=3^2-4.1.(-10)
delta=9+40
delta=49
x=-b-/+ raiz de delta/2a
x=-3-7/2.1
x=-10/2
x=-5
x=-3+7/2.1
x=4/2
x=2