Question

Resolva as equações
a)x²-49=0
b)x²-1=0
c)2x²-50=0
d)4x²-49=0
e)7x²-21=0
f)x²-5x+6=0
g)x²-8x +12=0
h)3x²-7X +2=0
i)2X²-7x=15
j)x²+3X-6=-8

Answer 1

a)x²-49=0
a= 1, b= 0, c= -49

∆= b² - 4.a.c
∆= 0² - 4.1.(-49)
∆= 196

x= -b±√∆ /2.a

x'= -0+14/2.1
x'= 14/2
x'= 7

x"= -14/2
x"= -7


b)x²-1=0
a= 1, b= 0, c= -1

∆= 0² - 4.1.(-1)
∆= 4


x= -b±√∆ /2.a

x'= 2/2.1
x'= 2/2
x'= 1

x"= -2/2
x"= -1

c)2x²-50=0

∆= 0² - 4.2.(-50)
∆= 400

x= -b±√∆ /2.a

x'= 400/2.2
x'= 400/4
x'= 100

x"= -400/4
x"= -100

d)4x²-49=0

∆= 0² - 4.4.(-49)
∆= 784

x= -b±√∆ /2.a

x'= 28/2.4
x'= 28/8
x'= 3,5

x"= -28/8
x"= -3,5

e)7x²-21=0

∆= 0² - 4.7.(-21)
∆= 588

x= -b±√∆ /2.a

x'≈ 24,2/2.7
x'≈ 24,2/14
x'≈ 1,7

x"≈ -24,2/14
x"≈ -1,7

f)x²-5x+6=0
a= 1, b= -5, c= 6

∆= (-5)² - 4.1.6
∆= 25-24
∆= 1

x= -b±√∆ /2.a

x'= 5+1/2.1
x'= 6/2
x'= 3

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

g)x²-8x +12=0

∆= (-8)² - 4.1.12
∆= 64 - 48
∆= 16

x= -b±√∆ /2.a

x'= 8+4/2.1
x'= 12/2
x'= 6

x"= 8-4/2
x"= 4/2
x"= 2

h)3x²-7X +2=0

∆= (-7)² - 4.3.2
∆= 49 - 24
∆= 25

x= -b±√∆ /2.a

x'= 7+5/2.3
x'= 12/6
x'= 2

x"= 7-5/6
x"= 2/6
x"= 1/3

i)2X²-7x=15
2x² - 7x - 15 = 0

∆= (-7)² - 4.2.(-15)
∆= 49 + 120
∆= 169

x= -b±√∆ /2.a

x'= 7+13/2.2
x'= 20/4
x'= 5

x"= 7-13/4
x"= -6/4
x"= -3/2

j)x²+3X-6=-8
x² + 3x - 6 + 8 = 0
x² + 3x + 2 = 0

∆= 3² - 4.1.2
∆= 9 - 8
∆= 1

x= -b±√∆ /2.a

x'= -3+1/2.1
x'= -2/2
x'= -1

x"= -3-1/2
x"= -4/2
x"= -2

Bons estudos! :)