Question

ME AJUDEEEEEEEEM, É MUITO IMPORTANTE.

Resolva as equações do 2° grau abaixo:

A. X² +3x( x -12) = 0
B. . ( x -5)² = x25 -9
C. (x -4)² +5x ( x-1) = 16
D. x² - 32= 32
E. ( x +9)² = 81

Answer 1

A. x² +3x( x -12) = 0

x^2 + 3x^2 - 36x = 0

4x^2 - 36x = 0

x . (4x - 36) = 0

x' = 0

4x - 36 = 0

4x = 36

x = 36/4

x = 9

x" = 9

S = { 0 , 9 }

B. ( x -5)² = x25 -9

(x - 5) . (x - 5) = 25x - 9

x^2 - 5x - 5x + 25 = 25x - 9

x^2 - 10x + 25 - 25x + 9 = 0

x^2 - 35x + 34 = 0

a = 1

b = -35

c = 34

Δ = b^2 - 4 . a . c

Δ = (-35)^2 - 4 . 1 . 34

Δ = 1225 - 136

Δ = 1089

x = -b ± √Δ /2 . a

x = -(-35) ± √1089 /2 . 1

x = 35 ± 33 /2

x' = 35 - 33 /2

x' = 2/2

x' = 1

x" = 35 + 33 /2

x" = 68/2

x" = 34

S = { 1 , 34 }

C. (x -4)² +5x ( x-1) = 16

(x - 4) . (x - 4) + 5x^2 - 5x = 16

x^2 - 4x - 4x + 16 + 5x^2 - 5x - 16 = 0

6x^2 - 8x + 16 - 5x - 16 = 0

6x^2 - 13x = 0

x . (6x - 13) = 0

x' = 0

6x - 13 = 0

6x = 13

x = 13/6

x" = 13/6

S = { 0 , 13/6}

D. x² - 32= 32

x^2 = 32 + 32

x^2 = 64

x = √64

x = ± 8

x' = -8

x" = 8

S = { -8 , 8 }

E. ( x +9)² = 81

(x + 9) . (x + 9) = 81

x^2 + 9x + 9x + 81 = 81

x^2 + 18x + 81 - 81 = 0

x^2 + 18x = 0

x . (x + 18) = 0

x' = 0

x + 18 = 0

x = -18

x" = -18

S = { 0 , -18 }