Question

8)2x²-3x=2x-1
9)5x²-x+1=x+4x²
10)x²-2x+3=-12+6x
11)4x²+7x+3=2x²+2x
12)x(x+2)=3
13)x(x-5)+10=4
14)2x(4x-1)=21

Answer 1

8)2x²-3x=2x-1
2X² - 3X = 2X - 1
2X² - 3X - 2X + 1 = 0
2x² - 5x + 1= 0
a = 2
b = - 5
c = 1
Δ = b² - 4ac
Δ = (-5)² - 4(2)(1)
Δ = + 25 - 8
Δ = 17  ---------------------> √Δ = √17
se
Δ > 0 ( duas raizes diferentes)
baskara
x = - b + √Δ/2a
        -5 - √17                  -5 √17
x' = ----------------  = ---------------
          2(2)                       4
     
          - 5 + √17       - 5 + √ 17
x" = -------------- = -----------------
            2(2)                  4


9)5x²-x+1=x+4x²

5x²-x+1=x+4x²
5x² - x +  1 - x - 4x² = 0
5x² - 4x² - x - x + 1 = 0
1x² - 2x + 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
se
Δ = 0 ( unica OU duas raizes iguais)
x = - b/2a
x' e x" = -(-2)/2(1)
x' e x" = +2/2
x' e x" = 1

10)x²-2x+3=-12+6x

x²-2x+3=-12+6x
x² - 2x + 3 + 12 - 6x = 0
x² - 2x - 6x + 3 + 12 = 0
x² - 8x + 15 = 0
a = 1
b = - 8
c = 15
Δ = b² - 4ac
Δ = (-8)² - 4(1)(15)
Δ = + 64 - 60
Δ = 4 --------------------> √Δ= 2  porque √4 = 2
se
Δ > 0 ( duas raizes diferentes)
(baskara)

x = - b + √Δ/2a
x' =  - 8 - √4/2(1)
x' = - 8 - 2/2
x' = - 10/2
x' = - 5
e
x" = - 8 +√4/2(1)
x" = - 8 + 2/2
x" = - 6/2
x" = - 3

11)4x²+7x+3=2x²+2x
4x²+7x+3=2x²+2x

4x² + 7x + 3 - 2x² - 2x = 0
4x² - 2x² + 7x - 2x + 3 = 0
2x² + 5x + 3 = 0
a = 2
b = 5
c = 3
Δ = b² - 4ac
Δ = 5² - 4(2)(3)
Δ = 25 - 24
Δ = 1  ------------------> √Δ= 1 poruqe √1 = 1
Δ > 0 ( duas raizes diferentes)
(baskara)

x = - b + √Δ/2a
x' = -5 - √1/2(2)
x' = - 5 - 1/4
x' = - 6/4 (divide AMBOS por 2)
x' = - 3/2
e
x" - 5 + √1/2(2)
x" = - 5 +1/4
x" = -4/4
x" = - 1


12)x(x+2)=3

x(x+2)=3
x² + 2x = 3 
x² + 2x - 3 = 0
a = 1
b = 2
c = - 3
Δ = b² - 4ac
Δ = 2² - 4(1)(-3)
Δ = 4 + 12
Δ = 16 ------------------> √Δ = 4 porque √16 = 4
Δ > 0 ( duas raizes diferentes)
(baskara)

x = - b + √Δ/2a
x' = -2 - √16/2(1)
x' = - 2 - 4/2
x' = -6/2
x' = - 3
e
x"  = - 2 +√16/2(1)
x" = - 2 + 4/2
x" = 2/2
x" = 1

13)x(x-5)+10=4
x(x-5)+10=4
x² - 5x + 10 = 4
x² - 5x + 10 - 4 = 0
x² - 5x + 6 = 0

a = 1
b = - 5
c = 6
Δ = b² - 4ac
Δ = (-5)² - 4(1)(6)
Δ = +25 - 24
Δ = 1 =======> √Δ = 1    porque √1 = 1
Δ > 0 ( duas raizes diferentes)
(baskara)

x = - b + √Δ/2a
x' = -(-5) - √1/2(1)
x' = + 5 - 1/2
x' = 4/2
x' = 2
e
x" =  -(-5) + √1/2(1) 
x" = + 5 + 1/2
x" = 6/2
x" = 3

14)2x(4x-1)=21
2x(4x-1)=21

8x² - 2x = 21 

8x² - 2x - 21 = 0
a = 8
b = - 2
c = - 21
Δ = b² - 4ac
Δ = (-2)² - 4(8)(-21)
Δ = + 4 + 672
Δ = 676  ===============> √Δ = 26  porque √676 = 26
se
Δ > 0 DUAS  raizes diferentes
(baskara)
x = - b + √Δ/2a
x' = -(-2) - √676/2(8)
x' = + 2 - 26/16
x' = -24/16  (divide AMBOS por 8)
x' = - 3/2
e
x" = -(-2) + √676/2(8)
x" = + 2 + 26/16
x" =28/16   (divide AMBOS por 4)
x" = 7/4