\(\left(x^2+1\right)^2=4\left(2x-1\right)\)
\(\Rightarrow x^4+2x^2+1=8x-4\)
\(\Rightarrow x^4+2x^2+1-8x+4=0\)
\(\Rightarrow x^4+2x^2-8x+5=0\)
\(\Rightarrow x^4-x^2+3x^2-3x-5x+5=0\)
\(\Rightarrow x^2\left(x^2-1\right)+3x\left(x-1\right)-5\left(x-1\right)=0\)
\(\Rightarrow x^2\left(x-1\right)\left(x+1\right)+3x\left(x-1\right)-5\left(x-1\right)=0\)
\(\Rightarrow\left(x-1\right)\left(x^3+x^2+3x-5\right)=0\)
\(\Rightarrow\left(x-1\right)\left(x^3-x^2+2x^2-2x+5x-5\right)=0\)
\(\Rightarrow\left(x-1\right)\left[x^2\left(x-1\right)+2x\left(x-1\right)+5\left(x-1\right)\right]=0\)
\(\Rightarrow\left(x-1\right)^2\left(x^2+2x+5\right)=0\)
Ta thấy x2 ≥ 0 với mọi x
⇒ x2 + 2x + 5 > 0 với mọi x
\(\Rightarrow\left(x-1\right)^2=0\)
\(\Rightarrow x-1=0\Rightarrow x=1\)
Chúc bạn học tốt!
