Question

1 ) a) 7.(x+2)=5.(x-6)-14

2) a) 4x²-4x-3=0

b)x²+5x+6=0

c)x²-13+36=0

d) x²-45x+324=0

e) x²-29x+100=0 

Answer 1

1a) 7(x+2) = 5(x-6) - 14
7x + 14 = 5x - 30 - 14
7x + 14 = 5x - 44
7x - 5x = -44 - 14
2x = 58
x = 58/2
 x = 29

2)a) 4x² - 4x - 3 = 0
      a = 4
      b = - 4
      c = - 3
Δ = b² - 4ac
Δ = (-4)² - 4(4)(-3)
Δ = 16 + 48
Δ = 64 ------------√Δ = 8 =========> √64 = 8
se
Δ > 0 duas raízes diferentes
x = - b - + √Δ/2a
x' = -(-4) - √64/2(4)
x' = + 4 - 8/8
x' = -4/8 -------------divide ambos por 4
x' = -1/2
e
x" = -(-4) + √64/2(4)
x" = + 4 + 8/8
x" = 12/8---------divide AMBOS por 4
x" = 3/2

V = { -1/2 ; 3/2}

2b)
x² + 5x + 6 = 0
a = 1
b = 5
c = 6
 Δ = b² - 4ac
Δ = 5² - 4(1)(6)
Δ = 25 - 24
Δ = 1-----------√Δ = 1 ====> √1 = 1
se
Δ > 0 duas raízes diferentes
x = - b - + √Δ/2a
x' = - 5 - √1/2(1)
x' = -5-1/2
x' = -6/2
x' = - 3
e
x" = - 5 + √1/2(1)
x" = -5+1/2
x" = - 4/2
x" = -2
V = { - 3: - 2}

2c)
x² - 13x + 36 = 0
a = 1
b = - 13
c = 36
Δ = b² - 4ac
Δ = (-13)² - 4(1)(36)
Δ = 169 - 144
Δ  = 25 ------------√Δ= 25 ========> √25 = 5
x = - b - + √Δ/2a
x' = -(-13) - √25/2(1)
x' = + 13 - 5/2
x' = 8 /2
x'= 4
e
x" = -(-13) + √25/2(1)
x" = + 13 + 5/2
x" = 18/2
x"  9
V = { 4 ;9}

2 d)

x² - 45x + 324 = 0
a = 1
b = - 45
c = 324
Δ = b² - 4ac
Δ = (-45)² - 4(1)(324)
Δ = 2025 - 1296
Δ = 729-------------√Δ = 27 ========> √729 = 27
x = - b - + √Δ/2a
x' = -(-45) - √729/2(1)
x' = + 45 - 27/2
x' = 18/2
x' = 9
e
x" = -(-45) + √729/2(1)
x" = + 45 + 27/2
x" = 72/2
x" = 36
V= { 9; 36}