Question

Alguem pra me ajudar?

resolva a equaçao do 2 grau

a) -x²+3x-2=0

b)2x²-5x+2=0​​

Answer 1

a)

$- x {}^{2} + 3x - 2 = 0 \: \: . \: ( - 1)\\ x {}^{2} - 3x + 2 = 0$

$\boxed{a = 1 \: ,\: b = - 3 \: ,\: c = 2}$

$x = \frac{ - b± \sqrt{b {}^{2} - 4ac } }{2a} \\ x = \frac{ - ( - 3)± \sqrt{( - 3) {}^{2} - 4 \: . \: 1 \: . \: 2} }{2 \: . \: 1} \\ x = \frac{3± \sqrt{9 - 8} }{2} \\ x = \frac{3± \sqrt{1} }{2} \\ x = \frac{3±1}{2} \\ x = \frac{3 + 1}{2} = \frac{4}{2} = \boxed{2} \\ x = \frac{3 - 1}{2} = \frac{2}{2} = \boxed{1}$

$\boxed{S = \left \{1\: , \:2\right \}}$

b)

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

$\boxed{a = 2 \: ,\: b = - 5 \: , \: c = 2}$

$x = \frac{ - b± \sqrt{b {}^{2} - 4ac } }{2a} \\ x = \frac{ - ( - 5)± \sqrt{( - 5) {}^{2} - 4 \: . \: 2 \: . \: 2} }{2 \: . \: 2} \\ x = \frac{5± \sqrt{25 - 16} }{4} \\ x = \frac{5± \sqrt{9} }{4} \\ x = \frac{5±3}{4} \\ x = \frac{5 + 3}{4} = \frac{8}{4} = \boxed{2} \\ x = \frac{5 - 3}{4} = \frac{2}{4} \: : (2) = \boxed{ \frac{1}{2} }$

$\boxed{S = \left \{ \frac{1}{2} \: , \:2\right \}}$

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