x^6+2010-(x^4+x²+2009)
=x^6-x^4-x²+1
=x^4(x²-1)-(x²-1)
=(x^4-1)(x²-1)
=(x²+1)(x²-1)²
x²+1>0
x²-1>=0,当x=±1时等于0,x≠±1时大于0
所以
x=±1,x^6+2010=x^4+x²+2009
x≠±1,x^6+2010>x^4+x²+2009
x^6+2010-(x^4+x²+2009)
=x^6-x^4-x²+1
=x^4(x²-1)-(x²-1)
=(x^4-1)(x²-1)
=(x²+1)(x²-1)²
x²+1>0
x²-1>=0,当x=±1时等于0,x≠±1时大于0
所以
x=±1,x^6+2010=x^4+x²+2009
x≠±1,x^6+2010>x^4+x²+2009