Question

Resolva no conjunto R as seguintes equações irracionais :
a)√(3X+1) = 5
b) 2+√(3X+1) = 6
c)√(8X+1) - X = 2
d)√(5X+1) = X - 1

Answer 1

a
V(3x + 1)² = 5²
3x + 1 = 25
3x = 25 - 1
3x = 24
x = 8 ****
b
2 + V(3x + 1) = 6
V(3x + 1 ) = 6 - 2
V(3x + 1) = 4
(V(3x + 1)² = 4²
3x + 1 = 16
3x = 16 - 1
3x = 15
x = 5 ****

c
V(8x + 1) = 2 + x
V(8x + 1)² = ( 2 + x)²
8x + 1 = 2² + 2*2*x + x²
8x + 1 = 4 + 4x + x²
8x + 1 - 4 - 4x - x² = 0
-x² + 4x - 3 = 0
x² - 4x + 3 = 0
delta = 16 - 12 = 4 ou +-V4 = +-2 ****

x = ( 4 +-2)/2 
x1 = 6/2 = 3 ****
x2 = 2/2 = 1 ****

d
V(5x + 1) = ( x - 1 )
V(5x + 1)² = ( x - 1)²
5x + 1 = x² - 2*x*1 + 1²
5x + 1 = x² - 2x + 1
5x + 1 - x² + 2x - 1 = 0
-x² + 7x = 0
x² - 7x = 0
x( x - 7 ) = 0
x = 0 ***
x - 7 = 0
x = 7 ****

Answer 2

a)√(3X+1) = 5 ==> ( √(3X+1)² = 5² ==> 3x + 1  = 25

3x = 25 -1 ==> 3x = 24 ==> x = 8
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b) 2+√(3X+1) = 6 ==> √(3X+1) = 6 - 2 ==> √(3X+1)² = 4²
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3x + 1 = 16 ==> 3x = 16 -1 ==> 3x = 15 ==> x = 5
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c)√(8X+1) - X = 2  ==> √(X+1)² = (2 + x)²

8x + 1 = x² + 4x + 4 ==>  x² + 4x + 4 - 8x - 1 = 0 ==> x² - 4x + 3  = 0

Δ= (-4)² - 4.1.3 =  16 - 12 ==> 4                                       √4  =  2

x = 4+/-2 ==> x1 = 4+2 ==> x1 = 3   ; x2 = 4-2 ==> x2 = 1
         2                      2                                   2
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d)√(5X+1) = X - 1 ==> √(5x+1)² = (x - 1)²

5x + 1 = x² - 2x + 1 ==>  x² - 2x + 1 - 5x - 1 = 0 ==> x² - 7x = 0

x(x - 7) = 0

x1 = 0

x2 - 7 = 0 ==> x2 = 7 

Resposta só serve 7.