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
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
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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