Question

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1)fatore o trinômio e resolva as equações


a) x^2-2x+1=4

b)x^2+6x+9=49

c)4y^2-4y+1=25

d)9z^2+12z+4=64

2)determine um número cujo quadrado de sua soma com 3 resulte em 36.

Answer 1

a)$x^2-2x+1=4$
$x^2-2x+1-4$
$x^2-2x-3$
$(x+1)(x-3)$

b)$x^2+6x+9=49$
$x^2+6x+9-49$
$x^2+6x-40$
$(x+10)(x -4)$

c)$4y^2-4y+1=25$
$4y^2-4y+1-25$
$4y^2-4y-24$
$4y(y+2)(y-3)$

d)$9z^2+12z+4=64$
$9z^2 + 12z + 4 - 64$
$9z^2 + 12z -60$
$3(3z+10)(z-2)$


2)

$(x + 3)^2 = 36$

(x + 3) . (x + 3) = 36

$x^2 + 3x + 3x + 9 = 36$

$x^2 + 6x + 9 -36 = 0$

$x^2 + 6x - 27$

Delta = $b^2-4ac$
Delta = $6^2-4.1.(-27)$
Delta = $36+108$
Delta = $144$

x' = (-b + √144)/2a
x' = (-6 + 12)/2
x' = 6/2
x' = 3


Resposta:

x = 3

Comprovando:

$(x + 3)^2 = 36$
$(3 + 3)^2 = 36$
$6^2 = 36$
$36 = 36$

✔correto