Question

Resolva a equacao biquadrada sendo u=R X*4-3X²-18=0

Answer 1

Resposta:

$x^{4}-3x^{2}-18=0\\ \\atribua~a~incognita "y"~para~representar~x^{2}\\ \\(x^{2})^{2}-3x^{2}-18=0\\ \\y^{2}-3y-18=0\\ \\delta=b^{2}-4.a.c\\ \\delta=(-3)^{2}-4.1.(-18)\\ \\delta=9+72\\ \\delta=81\\ \\Formula~de~Bhaskara\\ \\y=\frac{-b+-\sqrt{delta}}{2.a}\\ \\y=\frac{3+-\sqrt{81}}{2}\\ \\y'=\frac{3+9}{2}=\frac{12}{2}=6\\ \\y''=\frac{3-9}{2}=-\frac{6}{2}=-3\\ \\para~y=6\\ \\x^{2}=y\\ \\x^{2}=6\\ \\x=\sqrt{6}\\ \\para~y=-3\\ \\x^{2}=y\\ \\x^{2}=-3\\ \\x=\sqrt{-3}~~(nao~pertence~ao~conjunto~dos~num~reais)$

Solução: x = √6