Question

Resolva as equações irracionais abaixo:
1) 2x=$\sqrt{9x-2}$
2) $\sqrt[3]{} \sqrt{3x+1} =2$

Answer 1

1 ) (2x)² = [ √ ( 9x - 2)]² ⇒4x² = 9x - 2 ⇒ 4x² -9x +2 = 0 
Δ= (-9)² - 4·4·2 = 81 - 32 = 49
x =  [- (-9)+- √49] / 2·4 ⇒ x = (9 +- 7) / 8 ⇒x' = (9-7)/8 ⇒x' = 1/4  e  
x'' = (9+7) / 8 = 16 / 8 = 2

2) {∛[√(3x+1)]}³= 2³ ⇒√(3x+1)=8 ⇒[√(3x+1)]² = 8² ⇒3x+1 = 64 ⇒3x=64-1⇒
3x=63 ⇒x = 21