Respostas
a)
3x²=0
3x² = 0
x² = 0/3
x² = 0
x = + √0
x' e x" = 0
S = {0}
b)
-9x²=0
-9x² = 0
x² = 0/-9
x² = - 0/9
x = + √0
x = 0
S = [0}
c)
4/7x²=0
4/7x² = 0
x² = 0/4/7
x² = 0
x = + √0
x = 0
S = {0}
d)
7x²-10=0
7x² - 10 = 0
7x² = 10
x² = 10/7
x = + √7/10
7 √7 √7.√10 √7.10 √70 √70
x = + √------- = -------- = ----------- = --------- = ------- = ------
10 √10 √10.√10 √10.10 √10² 10
x' = - √70/10
x" = + √70/10
e)
x²-81=0
x² - 81 = 0
x² = + 81
x = + √81
√81 = 9
x' = - 9
x" = + 9
f)
x²+64=0
x² + 64 = 0
x² = - 64
x = + √ - 64
Não possui raíz real, porque é um número negativo.
√-64
√-64 = √64(-1) = √64i²
√64i² = - 8i
√64i² = + 8i
g)
4/3x²-3=0
4/3x² - 3 = 0
4/3x² = 3
x² = 3/4/3
3 3 3 9
x² = ----------- = --- x ---- = ----
4 1 4 4
----
3
9
x² = -----
4
9 √9 3
x = + √----- = ------ ´= ------
4 √4 2
x' = - 3/2
x" = + 3/2
h)
2x²+6x=0
2x² + 6x = 0
2x(x + 3) = 0
2x = 0
x = 0/2
x' = 0
(x+3) = 0
x+3 = 0
x" = - 3
S = {-3; 0}
i)
-x²+x=0
-x² + x = 0
x(-x + 1) = 0
x' = 0
(-x +1) = 0
-x + 1 = 0
-x = - 1
x" = + 1
S = { 0; 1}
j)
3/5x²-x=0
3/5x² - x = 0
3/5x( x - 1) = 0
3/5x = 0
x = 0/3/5
x' = 0
(x-1) = 0
x - 1 = 0
x" = + 1
S = {0; 1}
k)
5x²+2/5x=0
5x² + 2/5x = 0
x(5x + 2/5) = 0
x = 0
(5x + 2/5)
5x + 2/5 = 0
5x = - 2/5
x = -2/5/5
2
- -------
5 2 1 2
x= ------------- = - --------x------ = - -------
5 5 5 25
S = { -2/25 : 0}
l)
-6/7x²+6/7x=0
6/7x(-x + 1) = 0
6/7x = 0
x = 0/6/7
x = 0
(-x+1) = 0
-x + 1 = 0
-x = - 1
x = + 1
S = { 0; 1}
Espero ter ajudado.