Question

Resolvas as equações irracionais.
a) √x+1 = 7
b) √3=x = √9-x
c) √2x-3 - √x+11 = 0
d) x-3 = 2√x
e) 2x = √9x-2
f) √x-3 = x-5

Answer 1

a) (√x+1)² = 7² ==> x + 1 = 49 ==> x = 49-1==> x = 48
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b) (√3+x) = (√9-x)²

3+x = 9 - x ==. x+x= 9-3 ==> 2x=6 ==> x = 3
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c) √2x-3 - √x+11 = 0 ==>  √2x-3  = √x+11 ==> (√2x-3)²  = (√x+11)² 

2x-3  = x+11 ==> 2x - x = 11+3 ==> x = 14
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d) x-3 = 2√x ==. (x-3)² = (2√x)²

x² - 6x + 9 = 4x ==> x² - 6x + 9 - 4x = 0 ==> x² - 10x + 9 = 0

x = 10+/-8
        2

x1 = 9   ; x2 = 1  
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e) (2x)² = (√9x-2)² ==> 4x² = 9x - 2 ==> 4x² - 9x + 2 = 0

x = 9+/-7
        16

x1 = 1      e  x2 =  2
                            16

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f) (√x-30² = (x-5)² ==> x - 3 = x² - 10x + 25 ==> x² - 10x + 25 - x + 3 = 0

x² - 11x + 28 = 0

x = 11+/-3
         2

x1 =  7    ;  x2 = 4