Question

Giải pt vô tỉ: x²-x-\(1000\sqrt{1+8000x}=1000\)

Answer 1

\(x^2-x-1000\sqrt{8000x+1}=1000\)

\(\Leftrightarrow\left(x^2-x-4002000\right)-\left(1000\sqrt{8000x+1}-4001000\right)=0\)

\(\Leftrightarrow\left(x-2001\right)\left(x+2000\right)-\frac{1000\left(8000x+1-4001^2\right)}{1000\sqrt{8000x+1}+4001000}=0\)

\(\Leftrightarrow\left(x-2001\right)\left(x+2000\right)-\frac{1000\cdot8000\left(x-2001\right)}{1000\sqrt{8000x+1}+4001000}=0\)

\(\Leftrightarrow\left(x-2001\right)\left(\left(x+2000\right)-\frac{1000\cdot8000}{1000\sqrt{8000x+1}+4001000}\right)=0\)

\(\Rightarrow x=2001\)

Answer 2

\(\)còn cái trong ngoặc thì sao