Question

Resolva as equações irracionais a seguir

Answer 1

a) 10+√(x+2) = x

√(x+2) = x-10

[√(x+2)]² = (x-10)²

x+2 = x²-20x+100

x²-21x+98 = 0

Δ = 49

x' = 21+7/2 = 28/2 = 14
x'' = 21-7/2 = 14/2 = 7

S{7;14}

b) √(26+x) - √(26-x) = 2

[√(26+x) -√(26-x)]² = 2²

(26+x)-2[√(26+x)(√(26-x)]+(26-x) = 2

-2[√(26+x)(√(26-x)] = 2-52

(-2[√(26+x)(√(26-x)])² = (-50)²

4(26+x)(26-x) = 2500

676-26x+26x-x² = 2500/4

676-x² = 625

x² = 676-625

x² = 51

x = +√51

ou

x = -√51