Question

若M是方程X²+X-1=0的实数根则代数式M³+2M²+2010=

Answer 1

M是方程X²+X-1=0的实数根 ∴M²+M-1=0 M^3+M^2-M=0 M^3+2M^2=M^2+M

∴M³+2M²+2010=M^2+M+2010=1+2010=2011