Question

Determine o conjunto solução de cada equação:
a) x²-15=0
b) 5x²+75x=0
c) 2x²-26x=0
d) x²+16=0
e) 2x²-200=0
f) 7x²+21x=0
g) 3x²-8x=0
h) 5x²-8x+3=x²+3

Answer 1

a) x² - 15 = 0 => x² = 15 => x = ± √15

b) 5.x² + 75.x = 0 => 5.x.(x + 15) => 5.x = 0 => x = 0 ou x + 15 = 0 => x = -15

c) 2.x² - 26.x = 0 => 2.x.(x - 26) => 2.x = 0 => x = 0 ou x - 26 = 0 => x = 26

d) x² + 16 = 0 => x² = -16 => x² = -16 => x = ± √-16 => ± 4.i (não é real).

e) 2.x² - 200 = 0 => 2.x² = 200 => x² = 100 => x = ±√100 => x = ±10

f) 7.x² + 21.x = 0 => 7.x.(x + 3) = 0 => 7.x = 0 => x = 0 ou x + 3 = 0 => x = -3

g) 3.x² - 8.x = 0 => x.(3.x - 8) = 0 => x = 0 ou 3.x - 8 = 0 => 3.x = 8 => x = 8/3

h) 5.x² - 8.x + 3 = x² + 3 => 4.x² - 8.x = 0 => 4.x.(x - 2) => 4.x = 0 => x = 0 ou x - 2 = 0 => x = 2

Answer 2

a) x² - 15 = 0 => x² = 15 => x = ± √15 (+3,-3)

b) 5.x² + 75.x = 0 => 5.x.(x + 15) => 5.x = 0 => x = 0 ou x + 15 = 0 => x = -15

c) 2.x² - 26.x = 0 => 2.x.(x - 26) => 2.x = 0 => x = 0 ou x - 26 = 0 => x = 26

d) x² + 16 = 0 => x² = -16 => x² = -16 => x = ± √-16 => ± 4.i (não é real).

e) 2.x² - 200 = 0 => 2.x² = 200 => x² = 100 => x = ±√100 => x = ±10

f) 7.x² + 21.x = 0 => 7.x.(x + 3) = 0 => 7.x = 0 => x = 0 ou x + 3 = 0 => x = -3

g) 3.x² - 8.x = 0 => x.(3.x - 8) = 0 => x = 0 ou 3.x - 8 = 0 => 3.x = 8 => x = 8/3

h) 5.x² - 8.x + 3 = x² + 3 => 4.x² - 8.x = 0 => 4.x.(x - 2) => 4.x = 0 => x = 0 ou x - 2 = 0 => x = 2