Question

Resolva a seguinte equação:
3x⁴ -8x²+5=0

Answer 1

$\Large\boxed{\begin{array}{l}\sf 3x^4-8x^2+5=0\\\sf 3(x^2)^2-8x^2+5=0\\\sf\Delta=b^2-4ac\\\sf\Delta=(-8)^2-4\cdot3\cdot5\\\sf\Delta=64-60\\\sf\Delta=4\\\sf x^2=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\\\sf x^2=\dfrac{-(-8)\pm\sqrt{4}}{2\cdot3}\\\\\sf x^2=\dfrac{8\pm2}{6}\begin{cases}\sf x^2=\dfrac{8+2}{6}=\dfrac{10\div2}{6\div2}=\dfrac{5}{3}\\\\\sf x^2=\dfrac{8-2}{6}=\dfrac{6}{6}=1\end{cases}\end{array}}$

$\Large\boxed{\begin{array}{l}\sf x^2=\dfrac{5}{3}\\\\\sf x=\pm\dfrac{\sqrt{5}}{\sqrt{3}}\cdot\dfrac{\sqrt{3}}{\sqrt{3}}\\\\\sf x=\pm\dfrac{\sqrt{15}}{3}\\\\\sf x^2=1\\\sf x=\pm\sqrt{1}\\\sf x=\pm1\\\\\sf S=\bigg\{-\dfrac{\sqrt{15}}{3},-1,1,\dfrac{\sqrt{15}}{3}\bigg\}\end{array}}$