Resolve as seguintes equações: e pare na equação.
a) 6x + 2x = 5 + x
b) x (2x + 3) = 1
c) x (x + 3) + 2x = 6
d) x +( x + 1)² = 3
e) x² =2(4x)
f) 2 (x²-1)= 3x
g) 4 (x² + x) = 1x²
h) x 2x + 3) = 1
Respostas
a)6x+2x = 5+x
8x-x = 5
7x = 5
x = 5/7
b)x(2x+3) = 1
2x²+3x-1 = 0
Δ = b²-4.a.c
Δ = 3²-4.2.(-1)
Δ = 9+8
Δ = 17
x = -b±√Δ/2.a
x = -3±√17/2.2
x = -3 ±√17/4
x' = -3+√17/4
x" = -3-√17/4
c)x(x+3)+2x = 6
x²+3x+2x = 6
x²+5x-6 = 0
Δ = b²-4.a.c
Δ = 5²-4.1.(-6)
Δ = 25+24
Δ = 49
x = -b±√Δ/2.a
x = -5±√49/2.1
x = -5±7/2
x'= -5+7/2 = 2/2 = 1
x"= -5-7/2 = -12/2 = -6
d)x+(x+1)² = 3
x+(x+1).(x+1) = 3
x+ x²+x+x+1 = 3
x²+3x+1-3 = 0
x²+3x-2 = 0
Δ = b²-4.a.c
Δ = 3²-4.1.(-2)
Δ = 9+8
Δ = 17
x = -b±√Δ/2.a
x = -3±√17/2.1
x = -3 ±√17/2
x' = -3+√17/2
x" = -3-√17/2
e)x² = 2(4x)
x² = 8x
x²-8x = 0
Δ = b²-4.a.c
Δ = (-8)²-4.1.0
Δ = 64
x = -b±√Δ/2.a
x = -(-8)±√64/2.1
x = 8±8/2
x' = 8+8/2 = 16/2 = 8
x" = 8-8/2 = 0/2 = 0
f)2(x²-1) = 3x
2x²-2 = 3x
2x²-3x-2 = 0
Δ = b²-4.a.c
Δ = (-3)²-4.2.(-2)
Δ = 9+16
Δ = 25
x = -b±√Δ/2.a
x = -(-3)±√25/2.2
x = 3±5/4
x' = 3+5/4 = 8/4 = 2
x" = 3-5/4 = -2/4 = -1/2
g)4(x²+x) = x²
4x²+4x-x² = 0
3x²+4x = 0
Δ = b²-4.a.c
Δ = 4²-4.3.0
Δ = 16
x = -b±√Δ/2.a
x = -4±√16/2.3
x = -4±4/6
x' = -4+4/6 = 0/6 = 0
x" = -4-4/6 = -8/6 = -4/3
h)x(2x+3) = 1
2x²+3x-1 = 0
Δ = b²-4.a.c
Δ = 3²-4.2.(-1)
Δ = 9+8
Δ = 17
x = -b±√Δ/2.a
x = -3±√17/2.2
x = -3 ±√17/4
x' = -3+√17/4
x" = -3-√17/4