令t=√2010,则x=1/2(t-1/t),x²+1=1/4(t-1/t)²+1=1/4(t+1/t)²,
所以x+√(x²+1)=1/2(t-1/t)+1/2(t+1/t)=t=√2010,
从而原式的值为2010.