Question

escreva na forma ax2 + bx + c = 0, denominada forma reduzida as seguintes equações do 2° grau.

a) x2 - 7 = x + 5

b) x2 + 11x = 16x - 6

c) (x-1)2 - (2x + 3)2 = 0

d) x (x - 6) + x2 = ( x - 5) (x + 2)

e) (x - 10)2 + x (x + 17) = 104

f) x2 - 1/3 = 1/6x2

g) x2/4 + 1/10 = x2/5 + x/2

h) x + 6 = 4x/x-2 (x ≠ 2)

j) 5/x - 3/x2 = 9/x-1 (x ≠ - 3, x ≠ 3)

Answer 1

a) x2 - 7 = x + 5⇒x²-x-7-5=0⇒  x²-x-12=0
  

b) x2 + 11x = 16x - 6⇒ x² +11x-16x+6=0⇒ x²-5x+6=0

c) (x-1)² - (2x + 3)² =  x²-2x+1-( 4x²+12x+9=0
x²-2x-4x²-12x-9=0⇒ -3x²-14x-9=0    se esse 2 realmente for expente.

d) x (x - 6) + x2 = ( x - 5) (x + 2)⇒ x²-6x+x²=x²-3x-10
x²-x²+x²-6x+3x -10=0⇒  x²-3x-10=0

e) (x - 10)2 + x (x + 17) = 104⇒ x²-20x+100+x²+17x-104=0⇒ 2x²-3x-4=0

f) x2 - 1/3 = 1/6x2⇒ x²-1/3= 1/6x²
x²-1/6x² -1/3 mmc=6
+6x²-x²-2=0⇒ 5x²+0x-2=0

g) x2/4 + 1/10 = x2/5 + x/2⇒ mmc=20
5x²+2=4x²+10x
5x²-4x²+10x+2=0⇒  x² +10x+2=0

h) x + 6 = 4x/x-2 (x ≠ 2)
(x+6).(x-2)=4x
x²-2x+6x-12-4x=0
x²+0x-12=0

j) 5/x - 3/x2 = 9/x-1 (x ≠ - 3, x ≠ 3)

Answer 2

Resposta:

) x2 - 7 = x + 5⇒x²-x-7-5=0⇒  x²-x-12=0

 

b) x2 + 11x = 16x - 6⇒ x² +11x-16x+6=0⇒ x²-5x+6=0

c) (x-1)² - (2x + 3)² =  x²-2x+1-( 4x²+12x+9=0

x²-2x-4x²-12x-9=0⇒ -3x²-14x-9=0    se esse 2 realmente for expente.

d) x (x - 6) + x2 = ( x - 5) (x + 2)⇒ x²-6x+x²=x²-3x-10

x²-x²+x²-6x+3x -10=0⇒  x²-3x-10=0

e) (x - 10)2 + x (x + 17) = 104⇒ x²-20x+100+x²+17x-104=0⇒ 2x²-3x-4=0

f) x2 - 1/3 = 1/6x2⇒ x²-1/3= 1/6x²

x²-1/6x² -1/3 mmc=6

+6x²-x²-2=0⇒ 5x²+0x-2=0

g) x2/4 + 1/10 = x2/5 + x/2⇒ mmc=20

5x²+2=4x²+10x

5x²-4x²+10x+2=0⇒  x² +10x+2=0

h) x + 6 = 4x/x-2 (x ≠ 2)

(x+6).(x-2)=4x

x²-2x+6x-12-4x=0

x²+0x-12=0

j) 5/x - 3/x2 = 9/x-1 (x ≠ - 3, x ≠ 3)

Explicação passo a passo: