Question

Resolva as equações.

A)
$\frac{ {x}^{2} }{3} + 3 - 2x = 0$
B)
$2 {x}^{2} - \frac{3x}{2} + \frac{1}{4} = 0$
C)
$\frac{x + 1}{2} - \frac{ {x}^{2} + 1}{3} = 0$
D)
$\frac{ {x}^{2} }{2} - \frac{1}{5} = \frac{3x - 1}{5}$

Answer 1

a)

$\frac{ {x}^{2} }{3} + 3 - 2x = 0$

MMC entre 3 e 1 = 3

$\frac{ {x}^{2} + 9 - 6x }{3} = 0$

multiplica cruzado

x² -6x +9 = 0

$x = \frac{ - b± \sqrt{ {b}^{2} - 4.a.c} }{2.a}$

a= 1

b= -6

c = 9

$x = \frac{ - ( - 6)± \sqrt{ {6}^{2} - 4.1.9 } }{2.1}$

$x = \frac{6± \sqrt{36 - 36} }{2}$

$x = \frac{6± \sqrt{0} }{2}$

x = 3

b)

${2x}^{2} - \frac{3x}{2} + \frac{1}{4} = 0$

MMC = 4

$\frac{ {8x}^{2} - 6x + 1 }{4} = 0$

8x² -6x +1 = 0

a = 8 b = -6 c = 1

$x = \frac{ - ( - 6)± \sqrt{ {6}^{2} - 4.8.1 } }{2.8}$

$x = \frac{6± \sqrt{36 - 32} }{16}$

$x = \frac{6± \sqrt{4} }{16}$

x1 = 6+2/16

x1 = 8/16 = 1/2

x2= 6-2/16

x2= 4/16

x2= 1/4

desculpa apertei responder sem querer mais vou terminar aqui

c)

x+1/2 - x²-1/3 = 0

MMC = a 6

3x +3 - x² +1 /6 = 0

-x²+3x +3 +1 = 0

-x² +3x +4 = 0 (-1)

x² -3x -4 =0

a = 1

b = -3

c = -4

x = -(-3) ± √ 3²-4.1.(-4)/2

x = 3±√9 +16/2

x= 3±√25/2

x1 = 3+5/2

x1 = 8/2

x1 = 4

x2 = 3-5/2

x2=-2/2

x2=-1


d

X²/2 -1/5 =3x-1/5

MMC = 10


5x² -2/10 = 3x -1 /5

25x² -10 = 30x -10

25x² -10+10 = 30X

25X² = 30X

25X²-30X = 0

X(25x -30) = 0

X1 = 0


X2=

25x = 30

X = 30/25

X2= 6/5