Resolva as equações completas no conjunto R:
a) 4x²-4x+1=0
b) x²-4x-12=0
c) x²+6x+9=0
d) 3x²+4x+2=0
e) y²-16y+64=0
f) 6x²-x-5=0
g) x²-6x-16=0
Soluções para a tarefa
Resposta:
Explicação passo-a-passo:
A)
4x² - 4x + 1 = 0
a = 4; b = - 4; c = 1
Δ = b² - 4ac
Δ = (-4)² - 4.4.1
Δ = 16 - 16
Δ = 0
a = 4; b = - 4; c = 1
x = - b +/- √Δ = - ( - 4) +/- √0
--------------- -------------------- = 4/8 = 1/2
2a 2.4
R.: x = 1/2
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
b)
x² - 4x - 12 = 0
a = 1; b = - 4; c = -12
Δ = b² - 4ac
Δ = (-4)² - 4.1.(-12)
Δ = 16 + 48
Δ = 64
a = 1; b = - 4; c = -12
x = - b +/- √Δ = - ( - 4) +/- √64
--------------- -------------------
2a 2.1
x = (4 + 8)/2 = 12/2 = 6
x = (4 - 8)/2 = - 4/2 = - 2
R.: x = 6 e x = - 2
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
c)
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)
3x² + x + 2 = 0
a = 3; b = 1; c = 2
Δ = b² - 4ac
Δ = 1² - 4.3.2
Δ = 1 - 12.2
Δ = 1 - 24
Δ = - 23 (não há solução para os Reais, pois Δ < 0)
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
e)
x² -16x + 64 = 0
a = 1; b = - 16; c = 64
Δ = b² - 4ac
Δ = (-16)² - 4.1.64
Δ = 256 - 256
Δ = 0
x = - b +/- √Δ = - ( - 16) +/- √0
---------------- ----------------------
2a 2.1
x = 16/2 ; x = 8
R.: x = 8
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
f)
6x² - x - 5 = 0
a = 6; b = - 1; c = - 5
Δ = b² - 4ac
Δ = (-1)² - 4.6.(- 5)
Δ = 1 - 4.(-30)
Δ = 1 + 120
Δ = 121
x = - b +/- √Δ = - ( - 1) +/- √121
---------------- -----------------------
2a 2.6
x = 1 + 11
------------ = 12/12 = 1
12
x = 1 - 11 - 10 (:2) - 5
---------- = ------- = ------
12 12 (:2) 6
R.: x = 1 e x = - 5/6
***********************
g)
x² - 6x - 16= 0
a = 1; b = - 6; c = - 16
Δ = b² - 4ac
Δ = (-6)² - 4.1.(-16)
Δ = 36 + 64
Δ = 100
x = - b +/- √Δ = - (-6) +/- √100
----------------- --------------------
2a 2.1
x = (6 + 10)/2 = 16/2 = 8
x = (6 - 10)/2 = - 4/2 = - 2