Question

${3x}^{4} = 243$
resolver la ecuación
​

Answer 1

Respuesta:

$x=3,\:x=-3,\:x=3i,\:x=-3i$

Explicación paso a paso:

$\frac{3x^4}{3}=\frac{243}{3}\\x^4=81\\u^2=81\\u=\sqrt{81},\:u=-\sqrt{81}\\\mathrm{Resolver\:}\:x^2=\sqrt{81}:\quad x=3,\:x=-3\\x^2=\sqrt{81}\\x^2=\sqrt{9^2}\\x^2=9\\x=\sqrt{9},\:x=-\sqrt{9}\\\sqrt{9}=3\\\sqrt{9}\\=\sqrt{3^2}\\\sqrt{3^2}=3\\=3\\-\sqrt{9}=-3\\-\sqrt{9}\\\sqrt{9}=3\\\sqrt{9}\\=\sqrt{3^2}\\\sqrt{3^2}=3\\=-3\\x=3,\:x=-3\\\mathrm{Resolver\:}\:x^2=-\sqrt{81}:\quad x=3i,\:x=-3i\\x^2=-\sqrt{81}\\\sqrt{81}=9\\\sqrt{81}\\=\sqrt{9^2}\\\sqrt{9^2}=9\\x^2=-9$$x=\sqrt{-9},\:x=-\sqrt{-9}\\\sqrt{-9}:\quad 3i\\\sqrt{-9}\\\sqrt{-9}=\sqrt{-1}\sqrt{9}\\=\sqrt{-1}\sqrt{9}\\=\sqrt{9}i\\\sqrt{9}=3\\\sqrt{9}\\=\sqrt{3^2}\\\sqrt{3^2}=3\\=3i\\-\sqrt{-9}:\quad -3i\\-\sqrt{-9}\\\sqrt{-9}:\quad 3i\\\sqrt{-9}\\\sqrt{-9}=\sqrt{-1}\sqrt{9}\\=\sqrt{-1}\sqrt{9}\\=\sqrt{9}i\\\sqrt{9}=3\\\sqrt{9}\\=\sqrt{3^2}\\=\sqrt{3^2}\\=3i\\=-3i\\x=3i,\:x=-3i\\x=3,\:x=-3,\:x=3i,\:x=-3i$