Question

Giải phương trình:

\(x^4-30x^2+31x-30=0\)

Answer 1

\(x^4-30x^2+31x-30=0\)

<=>\(x^4-30x^2+30x+x-30=0\)

<=>\(\left(x^4+x\right)-\left(30x^2-30x+30\right)=0\)

<=>\(x\left(x^3+1\right)-30\left(x^2-x+1\right)=0\)

<=>\(x\left(x+1\right)\left(x^2-x+1\right)-30\left(x^2-x+1\right)=0\)

<=>\(\left(x^2-x+1\right)\left(x^2+x-30\right)=0\)

<=>\(\left(x^2-x+1\right)\left[\left(x^2+6x\right)-5\left(x+30\right)\right]=0\)

<=>\(x^2\left(-x+1\right)\left[x\left(x+6\right)-5\left(x+6\right)\right]=0\)

<=>\(\left(x^2-x+1\right)\left(x+6\right)\left(x-5\right)=0\)

=>\(x+6=0hoặcx-5=0\) vì\(\left[x^2-x+1=\left(x-\dfrac{1}{2}\right)^2+\dfrac{3}{4}>0\right]\)

<=> x=-6 hoặc x=5

Vậy......