Question

若m=2011/根号2012-1，则m^5-2m^4-2011m^3的值是

若m=2011/根号2012-1，则m^5-2m^4-2011m^3的值是

Answer 1

m=2011/(根号2012-1)
=2011×(√2012+1)/(√2012-1)(√2012+1)
=2011×(√2012+1)/(2012-1)
=√2012+1
m^5-2m^4-2011m^3
=m³(m²-2m-2011)
=(√2012+1)³[(√2012+1)²-2*(√2012+1)-2011]
=(√2012+1)³(2012+2√2012+1-2√2012-2-2011)
=(√2012+1)³×0
=0

Answer 2

m=2011/(根号2012-1)=√2012+1
∴m-1=√2012
∴(m-1)²=2012
∴m²-2m-2011=0
m^5-2m^4-2011m^3
=m^3(m²-2m-2011)
=0