Question

Giải các phương trình: 

1. 𝑥^4 − 5𝑥 ^2 + 4 = 0

Answer 1

Ta có: \(x^4-5x^2+4=0\)

\(\Leftrightarrow\left(x^2-1\right)\left(x^2-4\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left(x-2\right)\left(x+1\right)\left(x+2\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=2\\x=-1\\x=-2\end{matrix}\right.\)

Vậy: S={1;2;-1;-2}

Answer 2

đặt \(t=x^2\left(t\ge0\right)=>t^2-5t+4=0\)

\(=>\Delta=\left(-5\right)^2-4.4=9>0\)

\(=>\left[{}\begin{matrix}t1=\dfrac{5+\sqrt{9}}{2}=4\left(tm\right)\\t2=\dfrac{5-\sqrt{9}}{2}=1\left(tm\right)\end{matrix}\right.\)

với \(t=t1=>x=\pm2\)

với \(t=t2=>x=\pm1\)