Question

Resolva a equação,na variável x: x² + 2x + sen a = 0

Answer 1

x² + 2x + sen a = 0

a = 1 ; b= 2 ; c = sen a

▲ = b² - 4ac 

▲ = 4 - 4*1*sen(a)

▲ = 4 - 4 sen a

x = -b ± √▲ / 2a

x = [-2 ± √4 - 4 sen a] / 2 = -2 ± √4(1 -  sen a) = (-2 ± 2 √1 -sen a)/2  = -1 ± √1 - sen a

x1 = -1 + (√1 - sen a)

x2 = -1 - (√1 -  sen a)

S = {-1 + (√1 - sen a) ; -1 - (√1 -  sen a) }

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12/12/2015
Sepauto - SSRC
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Answer 2

Vou resolver completando quadrados (note que (x + 1)² = x² + 2x + 1)

$x^{2}+2x+sen(a)=0\\\\x^{2}+2x+1+sen(a)-1=0\\\\(x+1)^{2}+sen(a)-1=0\\\\(x+1)^{2}=1-sen(a)\\\\\sqrt{(x+1)^{2}}=\sqrt{1-sen(a)}\\\\|x+1|=\sqrt{1-sen(a)}\\\\x+1=\pm\sqrt{1-sen(a)}\\\\\boxed{\boxed{x=-1\pm\sqrt{1-sen(a)}}}$