Question

$\sqrt{3x+6}=x+2$

Answer 1

Explicação passo-a-passo:

√3x+6 = x + 2

√(3x+6)² = (x + 2)²

3x + 6 = (x + 2).(x + 2)

3x + 6 = x² + 2x + 2x + 4

3x + 6 = x² + 4x + 4

- x² - 4x + 3x + 6 - 4 = 0 .(-1)

x² + 4x - 3x - 6 + 4 = 0

x² + x - 2 = 0

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∆ = b² - 4ac

∆ = 1² - 4.1.(-2)

∆ = 1 + 8

∆ = 9

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x = - b ± √∆/2a

x = - 1 ± √9/2.1

x = - 1 ± 3/2

x' = -1+3/2 = 2/2 = 1

x" = -1-3/2 = -4/2 = - 2

S = {- 2 ; 1}