Question

Qual o resultado? $q^{4}-q^{2}+2=0$

Answer 1

$ax^{2}+bx+c=0\\\\\Delta=b^{2}-4ac\\x=(-b\pm\sqrt{\Delta})/2a$
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$q^{4}-q^{2}+2=0\\(q^{2})^{2}-q^{2}+2=0$

É uma equação do segundo grau com variável q²

$\Delta=b^{2}-4ac\\\Delta=(-1)^{2}-4*1*2\\\Delta=1-8\\\Delta=-7\\\sqrt{\Delta}=\sqrt{-7}\\\sqrt{\Delta}=\sqrt{-1*7}\\\sqrt{\Delta}=\sqrt{-1}*\sqrt{7}\\\sqrt{\Delta}=i*\sqrt{7}\\\sqrt{\Delta}=i\sqrt{7}$

$q^{2}=(-b\pm\sqrt{\Delta})/2a\\q^{2}=(-[-1]\pm i\sqrt{7})/(2*1)\\q^{2}=(1\pm i\sqrt{7})/2\\\\\\(q')^{2}=(1+i\sqrt{7})/2\\q'=\pm\sqrt{(1+i\sqrt{7})/2}\\\\\\(q'')^{2}=(1-i\sqrt{7})/2\\q''=\pm\sqrt{(1-i\sqrt{7})/2}$

$\boxed{\boxed{S=\{\sqrt{\frac{1+i\sqrt{7}}{2}},~-\sqrt{\frac{1+i\sqrt{7}}{2}},~\sqrt{\frac{1-i\sqrt{7}}{2}},~-\sqrt{\frac{1-i\sqrt{7}}{2}}\}}}$