Question

Determine as raízes da equação: É só a questão 5

Answer 1

Oie, Td Bom?!

$( \frac{3m}{2} - 1) {}^{2} + ( \frac{m}{4} - 2) {}^{2} = 5$

$( \frac{3m}{2} ) {}^{2} - 2 \: . \: \frac{3m}{2} \: . \: 1 + 1 {}^{2} + ( \frac{m}{4} ) {}^{2} - 2 \: . \: \frac{m}{4} \: . \: 2 + 2 {}^{2} = 5$

$\frac{9m {}^{2} }{4} - \frac{6m}{2} + 1 + \frac{m {}^{2} }{16} - \frac{4m}{4} + 4 = 5$

$\frac{9m {}^{2} }{4} - 3m + 1 + \frac{m {}^{2} }{16} - m + 4 = 5$

$\frac{37}{16} m {}^{2} - 4m + 5= 5$

$\frac{37}{16} m {}^{2} - 4m = 0$

$m \: . \: ( \frac{37}{16} m - 4) = 0$

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$m = 0$

$\frac{37}{16} m - 4 = 0⇒m = \frac{64}{37}$

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$S = \left \{ m_{1} = 0 \: , \: m_{2} = \frac{64}{37} \right \}$

Att. Makaveli1996