Question

O conjunto verdade das equações irracionais passo a passo POR FAVOR
√2x+2=x+1
√x=x
2 √x+x2x
x- √2x+2=3

Answer 1

a)√2x+2=x+1
\/2x=x+1-2
\/2x=x-1
2x=x^2 -2x + 1
2x-x^2 + 2x - 1=0
4x - x^2 - 1= 0
-x^2 + 4x - 1 = 0
x^2 - 4x + 1 = 0
aplicando o delta
/\= - b+- \/ d - 4.a.c / 2.a
x= - (-4) +-\/(-4)^2 - 4 .1.1 / 2.1
x=4 +-\/16-4/2
x=4+-\/12 / 2
x = 4+2\/3 / 2
x1= 2+2\/3
x2=2-2\/3



b)√x=x
x=x^2
x - x ^2 = 0
x. (1 - x )=0
x=0
1 - x =0
x=0
x=1



c)2 √x+x2x
2\/x+x^2 . 2
2\/x . ( 1 + x\/x)
2\/x . ( 1 + \/x ) . ( 1 - 1\/x + x )
2\/x . ( 1 + \/x) . (1 - \/x +x)


d)x- √2x+2=3
- \/2x= 3 - x - 2
-\/2x = 1 - x
\/2x= -1 + x
2x= x^2 -2x + 1
2x - x^2 + 2x - 1 =0
4x - x^2 -1=0
-x^2 +4x -1 =0
x^2 - 4x + 1 =0
x= -4 +-\/(-4)^2 - 4.1.1 /2
x=4+-\/16-4/2
x=4+-\/12 /2
x=4+-2\/3 /2
x1=2+\/3
x2= 2-\/3