Dạng 2:
a: \(-x^4+2023x^2+2024=0\)
=>\(x^4-2023x^2-2024=0\)
=>\(x^4-2024x^2+x^2-2024=0\)
=>\(\left(x^2-2024\right)\left(x^2+1\right)=0\)
=>\(x^2-2024=0\)
=>\(x^2=2024\)
=>\(x=\pm2\sqrt{506}\)
b: \(2x^4-x^2-10=0\)
=>\(2x^4-5x^2+4x^2-10=0\)
=>\(x^2\left(2x^2-5\right)+2\left(2x^2-5\right)=0\)
=>\(\left(2x^2-5\right)\left(x^2+2\right)=0\)
=>\(2x^2-5=0\)
=>\(x^2=\dfrac{5}{2}=\dfrac{10}{4}\)
=>\(x=\pm\dfrac{\sqrt{10}}{2}\)
c: \(x^4-4x^2-12=0\)
=>\(x^4-6x^2+2x^2-12=0\)
=>\(x^2\left(x^2-6\right)+2\left(x^2-6\right)=0\)
=>\(\left(x^2-6\right)\left(x^2+2\right)=0\)
=>\(x^2-6=0\)
=>\(x^2=6\)
=>\(x=\pm\sqrt{6}\)
d: \(9x^4+5x^2-4=0\)
=>\(9x^4+9x^2-4x^2-4=0\)
=>\(\left(x^2+1\right)\left(9x^2-4\right)=0\)
=>\(9x^2-4=0\)
=>\(x^2=\dfrac{4}{9}\)
=>\(x=\pm\dfrac{2}{3}\)
e: \(x^4+x^2-6=0\)
=>\(x^4+3x^2-2x^2-6=0\)
=>\(x^2\left(x^2+3\right)-2\left(x^2+3\right)=0\)
=>\(\left(x^2+3\right)\left(x^2-2\right)=0\)
=>\(x^2-2=0\)
=>\(x^2=2\)
=>\(x=\pm\sqrt{2}\)
Dạng 2:
h:
ĐKXĐ: x<>0 và y<>0
\(\left\{{}\begin{matrix}\dfrac{2}{x}+\dfrac{3}{y}=-\dfrac{1}{4}\\\dfrac{3}{x}+\dfrac{4}{y}=-\dfrac{1}{2}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}\dfrac{6}{x}+\dfrac{9}{y}=-\dfrac{3}{4}\\\dfrac{6}{x}+\dfrac{8}{y}=-1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{1}{y}=-\dfrac{3}{4}-\left(-1\right)=\dfrac{1}{4}\\\dfrac{3}{x}+\dfrac{4}{y}=-\dfrac{1}{2}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y=4\\\dfrac{3}{x}=-\dfrac{1}{2}-\dfrac{4}{4}=-\dfrac{3}{2}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y=4\\x=-2\end{matrix}\right.\left(nhận\right)\)
i: ĐKXĐ: \(\left\{{}\begin{matrix}x>=-\dfrac{2}{3}\\y>=1\end{matrix}\right.\)
\(\left\{{}\begin{matrix}\sqrt{3x+2}-\sqrt{y-1}=\sqrt{2}\\-\sqrt{3x+2}+2\sqrt{y-1}=0\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}\sqrt{3x+2}-\sqrt{y-1}-\sqrt{3x+2}+2\sqrt{y-1}=\sqrt{2}\\\sqrt{3x+2}=2\sqrt{y-1}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}\sqrt{y-1}=\sqrt{2}\\\sqrt{3x+2}=2\sqrt{2}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y-1=2\\3x+2=8\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y=3\\x=2\end{matrix}\right.\left(nhận\right)\)