b: \(x^4-3x^2+2=0\)
=>\(x^4-x^2-2x^2+2=0\)
=>\(\left(x^2-1\right)\left(x^2-2\right)=0\)
=>\(\left[{}\begin{matrix}x^2-1=0\\x^2-2=0\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}x^2=1\\x^2=2\end{matrix}\right.\Leftrightarrow x\in\left\{1;-1;\sqrt{2};-\sqrt{2}\right\}\)
b: \(x^4-2x^2-3=0\)
=>\(x^4-3x^2+x^2-3=0\)
=>\(\left(x^2-3\right)\left(x^2+1\right)=0\)
mà \(x^2+1>=1>0\forall x\)
nên \(x^2-3=0\)
=>\(x^2=3\)
=>\(x=\pm\sqrt{3}\)
c: \(\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)=24\)
=>(x+1)(x+4)(x+2)(x+3)=24
=>\(\left(x^2+5x+4\right)\left(x^2+5x+6\right)=24\)
=>\(\left(x^2+5x\right)^2+10\left(x^2+5x\right)+24=24\)
=>\(\left(x^2+5x\right)^2+10\left(x^2+5x\right)=0\)
=>\(\left(x^2+5x\right)\left(x^2+5x+10\right)=0\)
=>x(x+5)=0
=>\(\left[{}\begin{matrix}x=0\\x=-5\end{matrix}\right.\)
d: \(x\left(x-1\right)\left(x^2-x+1\right)=6\)
=>\(\left(x^2-x\right)\left(x^2-x+1\right)-6=0\)
=>\(\left(x^2-x\right)^2+\left(x^2-x\right)-6=0\)
=>\(\left(x^2-x+3\right)\left(x^2-x-2\right)=0\)
mà \(x^2-x+3=\left(x-\dfrac{1}{2}\right)^2+\dfrac{11}{4}>=\dfrac{11}{4}>0\forall x\)
nên \(x^2-x-2=0\)
=>(x-2)(x+1)=0
=>\(\left[{}\begin{matrix}x=2\\x=-1\end{matrix}\right.\)
e: ĐKXĐ: x>=0
\(x+\sqrt{x}-2=0\)
=>\(x+2\sqrt{x}-\sqrt{x}-2=0\)
=>\(\left(\sqrt{x}+2\right)\left(\sqrt{x}-1\right)=0\)
mà \(\sqrt{x}+2>=2>0\forall x\)
nên \(\sqrt{x}-1=0\)
=>\(\sqrt{x}=1\)
=>x=1
f: ĐKXĐ: x>=0
\(x-2\sqrt{x}-3=0\)
=>\(x-3\sqrt{x}+\sqrt{x}-3=0\)
=>\(\left(\sqrt{x}-3\right)\left(\sqrt{x}+1\right)=0\)
mà \(\sqrt{x}+1>=1>0\forall x\)
nên \(\sqrt{x}-3=0\)
=>\(\sqrt{x}=3\)
=>x=9(nhận)
