Question

Resolva as equações por fatoração. a) x² – 4x + 4 = 4 b) x² – 10x + 25 = 1 c) x² + 16x + 64 = 9 d) x² – 14x + 49 = 16 e) x² + 20x + 100 = 25

Answer 1

Resposta:

a) $x_{1} = 0 \\x_{2} = 4$   b)  $x_{1} = 4 \\x_{2} = 6$   c)  $x_{1} = -5 \\x_{2} = -11$   d) $x_{1} = -3 \\x_{2} = -11$   e) $x_{1} = -5 \\x_{2} = -15$      

Explicação passo-a-passo:

a) x² – 4x + 4 = 4 => x² - 4x + 4 -4 = 0 => x² -4x = 0 => x (x - 4) =0 => x1 = 0

x -4 = 0 => x2 = 4

b) x² – 10x + 25 = 1 => x² - 10x + 25 -1 = 0 => x² - 10x + 22 = 0 => (x -4)(x - 6)=0

$x_{1} = x - 4 = 0 => x = 4$       $x_{2} = x - 6 = 0 => x_{2} = 6$      

c) x² + 16x + 64 = 9 =>x² + 16x + 64 - 9 =0 => x² + 16x + 55=0 (x + 5)(x + 11) = 0

$x_{1} = x + 5 = 0 => x_{1}= -5$    $x_{2} = x + 11 = 0 => x_{2} = -11$  

d) x² – 14x + 49 = 16  => x² – 14x + 49 -16 = 0 =>  x² – 14x + 33 = 0 =>

=> (x + 3)(x + 11) = 0

$x_{1} = x + 3 = 0 => x_{1}= -3$    $x_{2} = x + 11 = 0 => x_{2} = -11$

e) x² + 20x + 100 = 25 => x² + 20x + 100 -25 = 0 =>  x² + 20x + 75 = 0  =>

=> ( x + 5)( x + 15) = 0 =>

$x_{1} = x + 5 = 0 => x_{1}= -5$    $x_{2} = x + 15 = 0 => x_{2} = -15$