Question

Determine as raízes da equação x² – 4x + 5 = 0 no campo dos complexos.

Answer 1

Resposta:

x²-4x+5=0

x'=[4+√(16-20)]/2 = (4+√(-4)]/2= (4+2i)/4 =1 +i/2

x''=[4-√(16-20)]/2 = (4-√(-4)]/2= (4-2i)/4 =1 -i/2

Answer 2

Oie, Td Bom?!

$x {}^{2} - 4x + 5 = 0$

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$a = 1 \: ,\: b = - 4 \: , \: c = 5$

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$x = \frac{ - b± \sqrt{b {}^{2} - 4ac} }{2a}$

$x = \frac{ - ( - 4)± \sqrt{( - 4) {}^{2} - 4 \: . \: 1 \: . \: 5 } }{2 \: . \: 1}$

$x = \frac{4± \sqrt{16 - 20} }{2}$

$x = \frac{4± \sqrt{ - 4} }{2}$

$x = \frac{4± \sqrt{4 \: . \: ( - 1)} }{2}$

$x = \frac{4± \sqrt{4 } \sqrt{ - 1} }{2}$

$x = \frac{4± \sqrt{2 {}^{2} } i}{?}$

$x = \frac{4±2i}{2}$

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$x = \frac{4 + 2i}{2} = \frac{2(2 + i)}{2} = 2 + i$

$x = \frac{4 - 2i}{2} = \frac{2(2 - i)}{2} = 2 - i$

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$S= \left \{x_{1} = 2 + i \:, \: x_{2} = 2 - i \right \}$

Att. Makaveli1996