Question

Exercício: (4+2x)² - (2-x)²

Answer 1

= (4 + 2x)² - ( 2 - x)² 

= (16 + 2.4.2x + 4x²) - (4 - 2.2x + x²)

= 16 + 16x + 4x² - (4 - 4x + x²)
= 16 + 16x + 4x² - 4 + 4x - x²
= 16 - 4 + 16x + 4x + 4x² - x²
= 12 + 20x + 3x²
= 3x² + 20x + 12

Answer 2

(4 + 2x)² - (2 - x)²
(4 + 2x)(4 + 2x) - (2 - x)(2 - x)
16 + 8x + 8x + 4x² - (4 - 2x - 2x + x²)
16 + 16x + 4x² - 4 + 4x - x²
4x² - x² + 16x + 4x + 16 - 4
3x² + 20x + 12

3x² + 20x + 12 = 0

Delta = b² - 4ac
Delta = (20)² - 4(3)(12)
Delta = 400 - 144
Delta = 256

X = (-b +- raiz delta) / 2a
X = (-20 +- 16) / 2(3)
x' = (-20 + 16) / 6 = -4 / 6 = -2/3
x" = (-20 - 16) / 6 = -36 / 6 = -6

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