Question

a) 25x²=20x-4 b)2x=15-x² c)x²+3x-6=-8 d)4x²-x+1=x+3x² e)4+x(x-4)=x f)x(x+3)-40=0

Answer 1

a )

∆= b² - 4ac
∆= (-20)² - 4.25.4
∆= 400 - 400
∆= 0

Com ∆ sendo zero, as raízes serão iguais.

x= -b ± √∆ / 2a
x= -(-20) ± √0 / 2.25
x= 20/50
x'=x"= 0,4 

 

b) 2x=15 -x²
X²+2x-15=0
a=1
b=2
c=-15
▲=b²-4a.c
▲=(2)²-4(1).(-15)
▲=4+60
▲=64

x=-b±√▲/2.a
x=-2±8/2.1
x¹=6/2=3
x²=-10/2=-5
S={3,-5}

 

C)

x²+3x-6=-8
x²+3x-6+8=0
x²+3x+2=0
▲=b²-4ac
▲=3²-4x1x2
▲=9-8
 ▲= 1
x= -b+ou- raiz de delta
2a
x=3+1/2
x'=2
x=3-1/2
x"=1
S={2,1}

 

D)4x²-x+1=x+3x²
4xª-3xª-x-x+1=0
xª-2x+1=0
a=1, b=-2 e c=1
¤=bª-4ac
¤=(-2)ª-4.1.1
¤=4-4
¤=0
logo a equacao posui apenas uma rais.
x=-b/2a
x=-(-2)/2.1
x=2/2
x=1

 

E e a F nao sei fazer