Question

\(\left(1-2x\right)\sqrt{x^2+1}-2x^2-7x-1=0\)

Answer 1

ĐKXĐ: \(x\in R\)

\(\left(1-2x\right)\cdot\sqrt{x^2+1}-2x^2-7x-1=0\)

=>\(\left(1-2x\right)\cdot\sqrt{x^2+1}+2x-1-2x^2-9x=0\)

=>\(\left(1-2x\right)\left(\sqrt{x^2+1}-1\right)-x\left(2x+9\right)=0\)

=>\(\left(1-2x\right)\cdot\dfrac{x^2+1-1}{\sqrt{x^2+1}+1}-x\left(2x+9\right)=0\)

=>\(\left(1-2x\right)\cdot\dfrac{x^2}{\sqrt{x^2+1}+1}-x\left(2x+9\right)=0\)

=>\(x\left[\dfrac{x\cdot\left(1-2x\right)}{\sqrt{x^2+1}+1}-2x-9\right]=0\)

=>x=0(nhận)