Question

 Resolva as eguações irracionais :

a) √x+2 = 7

b) √5x-10 = √3x+2

c)3√x+8 = 20

d) ³√x²-x-4 =0

Answer 1

a)
$\sqrt{x+2}=7 \\ (\sqrt{x+2})^2=(7)^2 \\ x+2=49 \\ x=47$

b)
$\sqrt{5x-10} = \sqrt{3x+2 \\ } \\ (\sqrt{5x-10})^2 =( \sqrt{3x+2 \\ })^2 \\ 5x-10=3x+2 \\ 2x=12 \\ x=6$

c)
$3 \sqrt{ x+8}=20 \\ (3 \sqrt{ x+8})^2=(20)^2 \\ 9(x+8)=400 \\ 9x+72=400 \\ x= \frac{400-72}{9} = \frac{328}{9}$

d)
$\sqrt[3]{ x^{2}-x-4 }=0 \\ (\sqrt[3]{ x^{2}-x-4 })^3=(0)^3 \\ x^{2}-x-4=0 \\ x'= \frac{1+ \sqrt{17} }{2} \\ x"= \frac{1-\sqrt{17} }{2}$