Question

Escreva na forma geral e resolva na fórmula de bhaskára.
a) 13-2x-15x²=0
b) 4x²+7x+3=2x²+2x
c) x(2x-1)+6=4(x+1)
d)(x-1) (x-2)=6
e)(2x-3) (x-8)=34

Answer 1

a)-15 x² - 2 x + 13 = 0
Δ = b² - 4.a.c
Δ = (-2)² - 4 .-15 . 13
Δ = 4 + 780
Δ = 784 ⇒√ 784 = 28
x = - b + ou - 28 / 2 . -15
x = -(-2) + 28 / -30
x´= 2 + 28 / -30
x´= 30 / -30
x´=  -1
x´´ = 2 - 28/-30
x ´´= -26/-30
x´´ = 13/15
S = {13/15 ; -1}
b)4 x² + 7 x + 3 = 2 x² + 2 x
4 x² - 2 x² + 7 x - 2 x + 3 = 0
2 x² + 5 x  + 3 = 0
Δ = b² - 4 .a.c
Δ = 5² - 4 . 2.3
Δ = 25 - 24
Δ = 1 ⇒ √ 1 = 1
x = - b +ou - 1/2.2
x = - 5 + 1/4
x´= -4/4 ⇒ -1
x´´ = -5 - 1/4 
x´´ = -6/4 ⇒-3/2
S = {-3/2 ; -1}
c)x(2 x - 1 ) + 6 = 4(x + 1)
2 x² - 1 x + 6 = 4 x + 4
2 x² -1 x - 4 x + 6 - 4 = 0
2 x² - 5 x + 2 = 0
Δ = b² - 4 .a.c
Δ = -(-5)² - 4 .2.2
Δ = 25 - 16
Δ = 9 ⇒ √9 = 3
x = - b +ou - 3/2.2
x = -(-5) + 3/4
x´= 5 + 3/4
x´= 8/4 ⇒2
x´´ = 5 - 3/4
x´´ = 2/4 ⇒ 1/2
S = {1/2 ; 2}
d)(x - 1) (x - 2 ) = 6
x² - 3 x + 2 = 6
x² - 3 x + 2 - 6 = 0
x² - 3x - 4 = 0
Δ = b² - 4 .a.c
Δ = (-3)² - 4 .1.-4
Δ = 9 + 16
Δ = 25 ⇒ √25 = 5
x = - b + ou - 5/2.1
x = -(-3) + 5/2
x´= 3 + 5/2
x = 8/2 ⇒ 4
x´´ = 3 - 5/2
x´´ = -2/2 = -1
S = {-1 ; 4}
e)(2 x- 3)(x - 8 ) = 34
2 x² - 19 x + 24 = 34
2 x² - 19 x + 24 - 34 = 0
2 x² - 19 x - 10 = 0
Δ = b² - 4.a.c
Δ = (-19)² - 4 .2 . -10
Δ = 361 + 80
Δ = 441 ⇒√441 = 21
x = - b + ou - 21/2.2
x´= -(-19)  + 21 /4
x´= 19 + 21 /4
x´= 40/4 ⇒ 10
x´´ = 19 - 21 / 4
x´´ = -2/4 ⇒-1/2
S = {-1/2 ; 10}