Question

Resolva as seguintes equações:
A) x2 - 100=0
B) 5x2 - 45=0
C) x2 - 9x=0
D) 2x2 -16x=0

Answer 1

x²-100=0
x²=100
x=√100
x=-+10


5x²-45=0               (:5)
x²-9=0
x²=9
x=√9
x=-+3

Δ = b² -4ac
Δ = (-9)² -4 *1 * 0
Δ = 81 0
Δ = 81
x' = (-b + √∆)/ 2a
(-(-9) + 9)/2 * 1
(9 + 9)/2
18/2
9
x'' = (-b - √∆)/ 2a
(-(-9) - 9)/2 * 1
(9 - 9)/2
0/2
0

S={0,9}

2x²-16x=0
Δ = b² -4ac
Δ = (-16)² -4 *2 * 0
Δ = 256 0
Δ = 256
x' = (-b + √∆)/ 2a
(-(-16) + 16)/2 * 2
(16 + 16)/4
32/4
8
x'' = (-b - √∆)/ 2a
(-(-16) - 16)/2 * 2
(16 - 16)/4
0/4
0

S={0,8}

Answer 2

a) x^2 -100 = 0 ==> x^2 = 100 ==> x = raiz quadrada (100) ==> x = +/- 10
b) 5x^2  - 45 = 0 ==>  5x^2 = 45 ==> x^2 = 45/5 ==> x^2 = 9 ==> x = +/- 3
c) x^2 - 9x = 0 ==> x(x -9) ==>
x' = 0,
x'' ==> x-9 = 0 ==> x = 9
d) 2x^2  - 16x = 2x(x -8)
x' ==> 2x = 0 ==> x = 0,  x'' ==> x - 8 = 0 ==> x = 8