Question

Giải các phương trình 

a) x⁴ +8x² -9= 0

b) (x² -x)² +4( x² -x)-12=0

Answer 1

a, Ta có :

x⁴+8x²-9=0

x⁴+9x²-x²-9=0

x⁴-x²+9x²-9=0

x²(x²-1)+9(x²-10=0

(x²-1)(x²+9)=0

\(\Rightarrow x^2-1=0\Rightarrow x=1\)

\(\Rightarrow x^2+9=0\Rightarrow x=-3\)

b, k bt lm

 

Answer 2

b) \(\left(x^2-x\right)^2+4\left(x^2-x\right)-12=0\)

\(\Leftrightarrow\left(x^2-x+2\right)^2=16\)

\(\Leftrightarrow\left[{}\begin{matrix}x^2-x+2=4\\x^2-x+2=-4\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x^2-x-2=0\\x^2-x+6=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}\left(x-2\right)\left(x+1\right)=0\\loại\end{matrix}\right.\)

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