Question

Resolva:

A. x²+2x=5x+8
B. x²=7x-6
C. x²-7+6x=6x+13-x

Answer 1

a)

x² + 2x = 5x + 8
x² + 2x - 5x - 8 = 0
x² - 3x - 8 = 0

Δ = b² - 4.a.c
Δ = (-3)² - 4.(1).(-8)
Δ = 9 + 32
Δ = 41

x = -b +/- √Δ/2a
x = 3 +/- √41/2

b)

x² = 7x - 6
x² - 7x + 6 = 0

Δ = b² - 4.a.c
Δ = (-7)² - 4.(1).(6)
Δ = 49 - 24
Δ = 25

x = -b +/- √Δ/2a
x = 7 +/- 5/2
x' = 6
x'' = 1

c)

x² - 7 + 6x = 6x + 13 - x
x² - 7 + 6x - 6x - 13 + x = 0
x² - 7 - 13 + x = 0
x² + x - 20 = 0

Δ = b² - 4.a.c
Δ = (1)² - 4.(1).(-20)
Δ = 1 + 80
Δ = 81

x = -b +/- √Δ/2a
x = -1 +/- 9/2
x' = 4
x'' = -5