Giải phương trình vô tỉ: x^2-x-1000√(1 8000x)=100

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

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

⇔ \(\left( {x - 2001} \right)\left( {x + 2000} \right) - \frac{{1000.8000\left( {x - 2001} \right)}}{{1000\sqrt {8000x + 1} + 4001000}} = 0\)

⇔ \(\left( {x - 2001} \right)\left[ {\left( {x + 2000} \right) - \frac{{1000.8000}}{{1000\sqrt {8000x + 1} + 4001000}}} \right] = 0\)

Dễ thấy \(\left( {x + 2000} \right) - \frac{{1000.8000}}{{1000\sqrt {8000x + 1} + 4001000}} \ne 0\)

Suy ra: x – 2021 = 0

Hay x = 2021

Vậy x = 2021