Question

3)resolva a equação biquadrada x4-9x²+20=0

Answer 1

$x^4-9x^2+20=0$

$(x^2)^2-9x^2+20=0$

$y=x^2$:

$y^2-9y+20=0$

$y=\dfrac{-(-9)\pm\sqrt{(-9)^2-4\cdot1\cdot20}}{2\cdot1}=\dfrac{9\pm\sqrt{1}}{2}=\dfrac{9\pm1}{2}$

$y'=\dfrac{9+1}{2}=5$

$y"=\dfrac{9-1}{2}=4$

$x^2=5$ $=>$ $x=\pm\sqrt{5}$

$x^2=4$ $=>$ $x=\pm2$

$S=\{-\sqrt{5},-2,\sqrt{5},2\}$