resolva as equações do 2o grau incompletas a)5x^2+10X=0 B)-2x^2+100=0 C)-3x^2+6x=0 D)4x^2+2x-20=80+2x E)3x^2-x =0 F)5/3x^2=0 G)16X^2-5=0 H)-2X^2+7x=x-14x^2
Respostas
respondido por:
2
Resolva as equações do 2o grau incompletas
equação do 2º grau INCOMPLETA também tem DUAS raizes
a)5x^2+10X =
5x² + 10x = 0
5x(x + 2) = 0
5x = 0
x = 0/5
x = 0
(x + 2) = 0
x + 2 = 0
x = - 2
assim
x' = 0
x" = - 2
B)-2x^2+100=0
-2x² + 100 = 0
- 2x² = - 100
x² = -100/-2
x² = + 100/2 fatora 50 | 2
x² = 50 25| 5
x = + - 50 5| 5
1/ = 2.5.5
= 2.5²
x = + - √2.5² ( elimina a √(raiz quadrada) com o (²)
x = + - 5√2
assim
x' = - 5√2
x" = + 5√2
.
C)-3x^2+6x=0
- 3x² + 6x = 0
3x(-x + 2) = 0
3x = 0
x = 0/3
x = 0
(-x + 2) = 0
- x + 2 = 0
- x = - 2
x = (-)(-)2
x = + 2
assim
x' = 0
x" = 2
D)4x^2+2x-20=80+2x
4x² + 2x - 20 = 80 + 2x ( igualar a zero)
4x² + 2x - 20 - 80 - 2x = 0
4x² + 2x - 2x - 20 - 80 = 0
4x² 0 - 100 = 0
4x² - 100 = 0
4x² = + 100
x² = 100/4
x² = 25
x = + - √25 ( lembrando que √25 = 5)
x = + - 5
assim
x' = - 5
x" = + 5
E)3x^2-x =0
3x² - x = 0
x(3x - 1) = 0
x = 0
(3x - 1) = 0
3x - 1 = 0
3x = + 1
x = 1/3
assim
x' = 0
x" = 1/3
F)5/3x^2=0
5/3x² = 0
x² = 0/(5/3)
x² = 0
x' e x" = 0
G)16X^2-5=0
16x² - 5 = 0
16x² = + 5
x² = 5/16
x = + - √5/16
x = + - √5/√16 ( lembrando que √16 = 4)
x = + - √5/4
assim
√5
x' = - ------
4
√5
x" = -------
4
H)-2X^2+7x=x-14x^2
- 2x² + 7x = x - 14x² ( igualar a zero) atenção no sinal
-2x² + 7x - x + 14x² = 0
- 2x² + 14x² + 7x - x = 0
12x² + 6x = 0
6x(6x + 1)= 0
6x = 0
x = 0/6
x = 0
(6x + 1) = 0
6x + 1 = 0
6x = - 1
x = - 1/6
assim
x' = 0
x" = - 1/6
equação do 2º grau INCOMPLETA também tem DUAS raizes
a)5x^2+10X =
5x² + 10x = 0
5x(x + 2) = 0
5x = 0
x = 0/5
x = 0
(x + 2) = 0
x + 2 = 0
x = - 2
assim
x' = 0
x" = - 2
B)-2x^2+100=0
-2x² + 100 = 0
- 2x² = - 100
x² = -100/-2
x² = + 100/2 fatora 50 | 2
x² = 50 25| 5
x = + - 50 5| 5
1/ = 2.5.5
= 2.5²
x = + - √2.5² ( elimina a √(raiz quadrada) com o (²)
x = + - 5√2
assim
x' = - 5√2
x" = + 5√2
.
C)-3x^2+6x=0
- 3x² + 6x = 0
3x(-x + 2) = 0
3x = 0
x = 0/3
x = 0
(-x + 2) = 0
- x + 2 = 0
- x = - 2
x = (-)(-)2
x = + 2
assim
x' = 0
x" = 2
D)4x^2+2x-20=80+2x
4x² + 2x - 20 = 80 + 2x ( igualar a zero)
4x² + 2x - 20 - 80 - 2x = 0
4x² + 2x - 2x - 20 - 80 = 0
4x² 0 - 100 = 0
4x² - 100 = 0
4x² = + 100
x² = 100/4
x² = 25
x = + - √25 ( lembrando que √25 = 5)
x = + - 5
assim
x' = - 5
x" = + 5
E)3x^2-x =0
3x² - x = 0
x(3x - 1) = 0
x = 0
(3x - 1) = 0
3x - 1 = 0
3x = + 1
x = 1/3
assim
x' = 0
x" = 1/3
F)5/3x^2=0
5/3x² = 0
x² = 0/(5/3)
x² = 0
x' e x" = 0
G)16X^2-5=0
16x² - 5 = 0
16x² = + 5
x² = 5/16
x = + - √5/16
x = + - √5/√16 ( lembrando que √16 = 4)
x = + - √5/4
assim
√5
x' = - ------
4
√5
x" = -------
4
H)-2X^2+7x=x-14x^2
- 2x² + 7x = x - 14x² ( igualar a zero) atenção no sinal
-2x² + 7x - x + 14x² = 0
- 2x² + 14x² + 7x - x = 0
12x² + 6x = 0
6x(6x + 1)= 0
6x = 0
x = 0/6
x = 0
(6x + 1) = 0
6x + 1 = 0
6x = - 1
x = - 1/6
assim
x' = 0
x" = - 1/6
respondido por:
1
a)
5x^2+10X=0
5x² + 10x = 0
x.(5x + 10) = 0
x = 0
5x + 10 = 0
5x = - 10
x = - 10/5
x = - 2
R.: x = 0 e x = - 2
******************************
B)-2x^2+100=0
- 2x² + 100 = 0
- 2x² = - 100 (-1)
2x² = 100
x² = 100/2
x² = 50
x = √50
x = √25.√2
x = 5√2 e x = - 5√2
*****************************
C)
- 3x^2 + 6x = 0
- 3x² + 6x = 0
x(- 3x + 6) = 0
x = 0
- 3x + 6 = 0
6 = 3x
3x = 6
x = 6/3
x = 2
R.: x = 0 e x = 2
**************************************
D)
4x^2+2x-20=80+2x
4x² + 2x - 20 = 80 + 2x
4x² = 80 + 20 + 2x - 2x
4x² = 100
x² = 100/4
x² = 25
x = √25
x = +/- 5
R.: x = + 5 e x = - 5
******************************
E)3x^2-x =0
3x² - x = 0
x.(3x - 1) = 0
x = 0
3x - 1 = 0
3x = 1
x = 1/3
R.: x = 0 e x = 1/3
***************************
F)
5/3x^2=0
5 x² = 0
-----
3
5x² = 0.3
5x² = 0
x² = 0/5
x = 0
*******************************
G)16X^2-5=0
16x² - 5 = 0
16x² = 5
x² = 5
------
16
x = √5
------
√16
x = - √5/4 e x = √5/4
**********************************
H)
- 2X^2 + 7x = x - 14x^2
- 2x² + 7x = x - 14x²
- 2x² + 14x² + 7x - x = 0
12x² + 6x = 0
x(12x + 6) = 0
x = 0
12x + 6 = 0
12x = - 6 (:6)
2x = - 1
x = - 1/2
R.: x = 0 e x = -1/2
5x^2+10X=0
5x² + 10x = 0
x.(5x + 10) = 0
x = 0
5x + 10 = 0
5x = - 10
x = - 10/5
x = - 2
R.: x = 0 e x = - 2
******************************
B)-2x^2+100=0
- 2x² + 100 = 0
- 2x² = - 100 (-1)
2x² = 100
x² = 100/2
x² = 50
x = √50
x = √25.√2
x = 5√2 e x = - 5√2
*****************************
C)
- 3x^2 + 6x = 0
- 3x² + 6x = 0
x(- 3x + 6) = 0
x = 0
- 3x + 6 = 0
6 = 3x
3x = 6
x = 6/3
x = 2
R.: x = 0 e x = 2
**************************************
D)
4x^2+2x-20=80+2x
4x² + 2x - 20 = 80 + 2x
4x² = 80 + 20 + 2x - 2x
4x² = 100
x² = 100/4
x² = 25
x = √25
x = +/- 5
R.: x = + 5 e x = - 5
******************************
E)3x^2-x =0
3x² - x = 0
x.(3x - 1) = 0
x = 0
3x - 1 = 0
3x = 1
x = 1/3
R.: x = 0 e x = 1/3
***************************
F)
5/3x^2=0
5 x² = 0
-----
3
5x² = 0.3
5x² = 0
x² = 0/5
x = 0
*******************************
G)16X^2-5=0
16x² - 5 = 0
16x² = 5
x² = 5
------
16
x = √5
------
√16
x = - √5/4 e x = √5/4
**********************************
H)
- 2X^2 + 7x = x - 14x^2
- 2x² + 7x = x - 14x²
- 2x² + 14x² + 7x - x = 0
12x² + 6x = 0
x(12x + 6) = 0
x = 0
12x + 6 = 0
12x = - 6 (:6)
2x = - 1
x = - 1/2
R.: x = 0 e x = -1/2
larisinha12:
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