Question

resolva as equaçoes para U=R:
a) x£- 5x² + 4 = 0

obs: nao consegui por o 4 pequeno encima do primeiro x mais seria a) x4 so que x elevado ao 4 pequeno

Answer 1

$\large\boxed{\begin{array}{l}\rm x^4-5x^2+4=0\\\rm (x^2)^2-5x^2+4=0\\\underline{\sf fac_{\!\!,}a}\\\rm x^2=y,com\,y\geqslant0.\\\rm y^2-5y+4=0\\\rm\Delta=b^2-4ac\\\rm\Delta=(-5)^2-4\cdot1\cdot4\\\rm\Delta=25-16\\\rm\Delta=9\\\rm y=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\\\rm y=\dfrac{-(-5)\pm\sqrt{9}}{2\cdot1}\\\\\rm y=\dfrac{5\pm3}{2}\begin{cases}\rm y_1=\dfrac{5+3}{2}=\dfrac{8}{2}=4\\\rm y_2=\dfrac{5-3}{2}=\dfrac{2}{2}=1\end{cases}\end{array}}$

$\large\boxed{\begin{array}{l}\underline{\sf voltando\!:}\\\rm para\,y=4:\\\rm x^2=4\\\rm x=\pm\sqrt{4}\\\rm x=\pm2\\\rm para\,y=1\\\rm x^2=1\\\rm x=\pm\sqrt{1}\\\rm x=\pm1\\\rm S=\{-2,-1,1,2\}\end{array}}$