Question

a) x² - 6x + 5 = 0                                                          
 
 b) 3x² + 4x + 1 = 0     
c) x² - 8x + 16 = 0                                                      
 d) x² - 13x + 22 =0              
e) x2 + 8x² + 16x = 0                                           
 f) 5x2 - 15x² + 10x = 0            
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Answer 1

Resposta:

A) x² - 6x + 5 = 0            

a = 1

b = -6

c = 5

Δ=b^{2} -4.a.c

Δ=6^{2} +(-4).1.5

Δ=36+(-20)

Δ=16

x'=-(-6)+√16/(2.1)

x'=6+√16/2

x'= 6+4/2

x'=10/2

x'=5

x''=-(-6)-√16/(2.1)

x''= 6-√16/2

x''=6-4/2

x''=2/2

x''=1

S = {5,1}

B)

3x² + 4x + 1 = 0    

a = 3

b = 4

c = 1

Δ = -4² - 4 x 3 x 5

Δ = 16 - 4 x 3 x 5

Δ = 16 - 12 = 4

x = - b ± √Δ / 2a

x = - 4 ± √4 / 2 * 3

x1 = -4 + 2 = -2/6 = -2/6:2= -1/3

x2 = -4 - 2 = -6/6 = -1

S = {-1/3,-1}

C) x² - 8x + 16 = 0                

a = 1

b = -8

c = 16

Δ = -8² - 4 x 1 x 16

Δ = 64 - 4 x 1 x 16

Δ = 64 - 64

Δ = 0

x = - b ± √Δ / 2a

x1 = 8 + 0 = 8/2 = 4

x2 = 8 - 0 = 8/2 = 4

S = {4}

D)   x² - 13x + 22 =0      

a = 1

b = -13

c = 22

Δ = b² -4 .a . c  

Δ = (-13)² -4 . 1 . 22

Δ = 169 - 88

Δ = 81

x = - b ± √Δ / 2a

x1  = 13 + 9 = 22/2 = 11

x2 = 13 - 9 = 4/2 = 2

S = {11,2}

E)   x² + 8x² + 16x = 0

     x9² + 16x = 0

a = 9

b = 16

c = 0

Δ = (16)² - 4 x 9 x 0

Δ = 256

x = - b ± √Δ / 2a

x1 = - 16 + 16 = 0

x2 = -16 - 16 = -32/18 = -16/9

S = {0,-16/9}

F)  5x² - 15x² + 10x = 0

     

a = 5

b = -15

c = 10

Δ = (-15²) - 4 x 5 x 10

Δ = 225 - 4 x 5 x 10

Δ = 25

 x = - b ± √Δ / 2a

x1 = 15 + 5 = 20/10 =2

x2 = 15 - 5 = 10/10 = 1

S {2,1}