Me ajudem nessas Equações resolução por favor :)
Equação do Segundo Grau
a) 2x² - 7x = 15
b) 4x² + 9 = 12x
c) 2x² = - 12x - 18
d) 2x = 15 - x²
e) 4x² - x + 1 = x + 3x²
Respostas
a)
2x² - 7x
= 15
2x² - 7x
- 15 = 0
a = 2; b = - 7; c = - 15
Δ = b² - 4ac
Δ = (-7)² - 4.2.(-15)
Δ = 49 - 8.(-15)
Δ = 49 + 120
Δ = 169
x = - b +/- √Δ = - (-7) +/- √169
--------------- ----------------------
2a 2.2
x = (7 + 13)/4 = 20/4 = 5
x = (7 - 13) = - 6 (:2) - 3
----------- ------- = ------
4 4 (:2) 2
R.: x = 5 e x = - 3/2
*********************************
b)
4x² + 9 = 12x
4x²
- 12x + 9 = 0
a = 4; b = - 12; c = 9
Δ = b² - 4ac
Δ = (-12)² - 4.4.9
Δ = 144 - 16.9
Δ = 144 - 144
Δ = 0
x = - b +/- √Δ = - ( - 12) +/- √0
-------------- ---------------------
2a 2.4
x = 12 (:4) 3
----- = -------
8 (:4) 2
R.: x = 3/2
*****************************
c)
2x² = - 12x - 18
2x²
+ 12x + 18 = 0 (:2)
x² + 6x +
9 = 0
a = 1; b = 6; c = 9
Δ = b² - 4ac
Δ = 6² - 4.1.9
Δ = 36 - 36
Δ = 0
x = - b +/- √Δ = - 6 +/- √0
--------------- ----------------
2a 2.1
x = - 6/2 = - 3
R.: x = - 3
**************************************
d)
2x = 15 - x²
x² + 2x -
15 = 0
a = 1; b = 2; c = - 15
Δ = b² - 4ac
Δ = 2² - 4.1.(-15)
Δ = 4 + 60
Δ = 64
a = 1; b = 2; c = - 15
x = - b +/- √Δ = - 2 +/- √64
---------------- ----------------
2a 2.1
x = (- 2 + 8)/2 = 6/2 = 3
x = (-2 - 8)/2 = - 10/2 = - 5
R.: x = 3 e x = - 5
******************************
e)
4x² - x + 1 = x + 3x²
4x² - 3x² - x - x + 1 = 0
x² - 2x + 1 = 0
a = 1; b = - 2; c = 1
Δ =
b² - 4ac
Δ = (-2)²
- 4.1.1
Δ = 4 - 4
Δ = 0
a = 1; b = - 2; c = 1
x = - b +/- √Δ - ( - 2)
+/- √0
---------------- = --------------------
2a
2.1
x = 2/2 = 1
R.: x = 1