Question

Resolva:

a) √25x² + 10x = 0

b) (x + 3)(x +3) = 0

c) (x + 6)(9 + x) = 0

d) (x + 9)(6 + x) = 0

Answer 1

A) ax²+bx+c

Formula de baskara

x= -b+/-√b²-4ac/2.a

x= -10+/- √ 10²-4. 25.0/2.25

x= -10+/-√100/50

x'= -10+10/50 = 0/50=0

x''= -10-10/50= -20/50= -2/5

B) x²+6x+9 a raiz e -3

C) x²+15x+54 as raizes -6 e -9

D) e igual a letra c

Answer 2

a) √(25x² + 10x) = 0        (elevo ambos os lados ao quadrado ...) 

√(25x² + 10x)² = 0² 

25x² + 10x = 0 

5x.(5x + 2) = 0 

5x = 0 

x = 0/5

x' = 0 

5x + 2 = 0 

5x = -  2

x'' = - 2/5                                 S = { - 2/5 , 0 } 

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b) 

(x+3).(x+3) = 0 

(x+3)² = 0 

x² + 2.x.3 + 3² = 0 

x² + 6x + 9 = 0 

Δ = 36 - 36 

Δ = 0 

x = -6 +-√0/2
x = -6 +-0/2

x' = -6/2 
x' = - 3

x'' = -6/2
x'' = - 3                                        S = { - 3 }  

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c) 

(x+6) (9+x) = 0 

9x + x² + 54 + 6x = 0 

x² + 15x + 54 = 0 

Δ = 225 - 216 

Δ = 9 

x = - 15 +- √9/2
x = - 15 +-3/2 

x' = -15+3/2 
x' = - 12/2
x' =  - 6

x'' = - 15-3/2 
x'' = - 18/2 
x'' = - 9                                           S = { - 9 , - 6 } 

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d) 

(x+9) (6+x) = 0 

6x + x² + 54 + 9x = 0 

x² + 15x + 54 = 0 

Δ = 225 - 216 

Δ = 9 

x = - 15 +- √9/2
x = - 15 +-3/2 

x' = -15+3/2 
x' = - 12/2
x' =  - 6

x'' = - 15-3/2 
x'' = - 18/2 
x'' = - 9                                           S = { - 9 , - 6 }                                    ok