Como resolve equações biquadradas?a) x^4-3x² -4 =0.... Pergunta de ideia deCarolina17

Carolina17 @Carolina17

April 2020 1 95 Report

Como resolve equações biquadradas?
a) x^4-3x² -4 =0

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adrielcavalcant $x^{4} - 3 x^{2} - 4 = 0\\\\
\boxed{x^{4} = y^{2}}\\\\
y^{2} - 3y - 4 = 0\\\\
\Delta = b^{2} - 4ac\\\\
\Delta = (-3)^{2} - 4.1.(-4)\\\\
\Delta = 25\\\\
y' = \frac{-(-b) + \sqrt{\Delta} }{2a} \\\\
y' = \frac{-(-3) + \sqrt{25} }{2} \\\\
y' = \frac{3 + 5}{2} = \frac{8}{2}\\\\
\boxed{y' = 4}$
$y'' = \frac{-(-3) - \sqrt{25} }{2} \\\\
y'' = \frac{3 - 5 }{2} \\\\
y'' = \frac{-2}{2}\\\\
\boxed{y'' = -1} \\\\
x^{4} = y^{2}\\\\
x^{2} = y\\\\
x^{2} = y'\\\\
x^{2} = 4\\\\
\boxed{x = \pm 2}\\\\
x^{2} = y''\\\\
x^{2} = -1\\\\
\boxed{x = \pm i}\\\\
\boxed{\boxed{S : {i,-i,-2,2}}}$

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