Question

solução da equação
$\sqrt{7x - 3 } - 1 = x$

Answer 1

[√(7x - 3)] - 1 = x
[√(7x - 3)] = x + 1
[√(7x - 3)]^2 = (x + 1)^2
7x - 3 = x^2 + 2x + 1
0 = x^2 + 2x + 1 + 3 - 7x
0 = x^2 - 5x + 4
x^2 - 5x + 4 = 0
a= 1; b = - 5; c = 4
∆ = b^2-4ac
∆ = (-5)^2 - 4.1.4
∆ = 25 - 16
∆ = 9

x = [ - b +/- √∆]/2a
x = [ -(-5) +/- √9]/2.1
x = [ 5 +/- 3]/2
x' = (5+3)/2 = 8/2 = 4
x" = (5-3)/2 = 2/2 = 1

Substituir:
x = 4
√(7x - 3) = x + 1
√(7.4 - 3) = 4 + 1
√(28-3) = 5
√25 = 5
5 = 5

x = 1
√(7x - 3) = x + 1
√(7.1 - 3) = 1 + 1
√(7 - 3) = 2
√4 = 2
2 = 2

R.: (4; 1)