Question

preciso de ajuda.....

Answer 1

a) x²/2 - 3 = 5x/2 (MMC = 2)
x² - 3*2 = 5x
x² - 5x - 6 = 0
& = [- 5]² - 4*1*[- 6] = 25 + 24 = 49
x1 = (- [+5] + v49) : 2*1 = [- 5 + 7] : 2 = 2/2 = 1
x2 = (- [+5] - v49) : 2*1 = [- 5 - 7] : 2 = - 12/2 = -6
x = {1, - 6}

b) 3x² - x/2 = - 2/3 (MMC = 6)
6*3x² - 3x = - 2*2
18x² - 3x = - 4
18x² - 3x + 4 = 0
& = [- 3]² - 4*18*4 = 9 - 288 = -279 (Não existe raiz real)

c) x²/2 = 3x - 5/2 (MMC = 2)
x² = 2*3x - 5
x² = 6x - 5
x² - 6x + 5 = 0
& = [-6]² - 4*1*5 = 36 - 20 = 16
x1 =  [- (- 6) + v16] : 2*1 = [6 + 4] : 2 = 10/2 = 5
x2 =  [- (- 6) - v16] : 2*1 = [6 - 4] : 2 = 2/2 = 1
x = {5, 1}

d) x² - x/3 = 8 (MMC =3)
3x² - x = 8*3 
3x² - x = 24 
3x² - x - 24 = 0
& = [- 1]² - 4*3*[-24] = 1 + 288 = 289
x1 = [- (- 1) + v289] : 2*3 = [1 + v289]/6
x2= [- (- 1) - v289] : 2*3 = [1 - v289]/6
x = {[1 + v289]/6, [1 - v289]/6}

e) x²/2 - 1/5 = [3x - 1]/5 (MMC = 10)
5x² - 2*1 = 2 [3x - 1]
5x² - 2 = 6x - 2
5x² - 2 - 6x + 2 = 0
5x² - 6x = 0
x [5x - 6] = 0
x1) x = 0 : [5x - 6] x = 0
x2)  5x - 6 = 0/x  5x - 6 = 0  5x = 6  x = 6/5
x = {0, 6/5}

f) x² + [28x - 4]/35 = x/7 (MMC = 35)
35x² + [28x - 4] = 5x
35x² + 28x - 4 - 5x = 0
35x² + 23x - 4 = 0
& = [23]² - 4*35*[-4] = 529 + 560 = 1089
x1 =[- 23 + v1089] : 2*35 = [- 23 + 33] : 70 = 10/70 = 1/7
x2= [- 23 - v1089] : 2*35 = [- 23 - 33] : 70 = -56/70 = - 4/5
x = {1/7, - 4/5}

g)[5x² + 3]/4 - [17 - x²]/2 = 8 (MMC = 4)
[5x² + 3] - 2[17 - x²] = 8*4
5x² + 3 - 34 + 2x² = 32
7x² = 32 + 34 - 3
7x² = 66 - 3
7x² = 63
x² = 63/7
x² = 9
x1 =  v9 = 3
x2 = v9 = - 3
x = {3, -3}

h) [x² - 2x]/4 = 1/4 + x/2 (MMC = 4)
x² - 2x = 1 + 2x
x² - 2x - 2x - 1 = 0
x² - 4x - 1 = 0
& = [- 4]² - 4*1[-1] = 16 + 4 = 20
x1 = [- (- 4) + v20] : 2*1 = [4 + 2v5]/2 = 2 + v5
x2 = [- ( -4) - v20] : 2*1 = [4 - 2v5]/2 = 2 - v5
x = {2 + v5, 2 - v5}