2,m是方程x²+x-1=0的根,则式子m三次方+2m²+2010的值是_______3,设a,b是方程x²+x-2010=0的两个实数根,则a²+2a+b的值是_______
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![2,m是方程x²+x-1=0的根,则式子m三次方+2m²+2010的值是_______3,设a,b是方程x²+x-2010=0的两个实数根,则a²+2a+b的值是_______](/uploads/image/z/11618834-50-4.jpg?t=2%2Cm%E6%98%AF%E6%96%B9%E7%A8%8Bx%26%23178%3B%2Bx-1%3D0%E7%9A%84%E6%A0%B9%2C%E5%88%99%E5%BC%8F%E5%AD%90m%E4%B8%89%E6%AC%A1%E6%96%B9%2B2m%26%23178%3B%2B2010%E7%9A%84%E5%80%BC%E6%98%AF_______3%2C%E8%AE%BEa%2Cb%E6%98%AF%E6%96%B9%E7%A8%8Bx%26%23178%3B%2Bx-2010%3D0%E7%9A%84%E4%B8%A4%E4%B8%AA%E5%AE%9E%E6%95%B0%E6%A0%B9%2C%E5%88%99a%26%23178%3B%2B2a%2Bb%E7%9A%84%E5%80%BC%E6%98%AF_______)
2,m是方程x²+x-1=0的根,则式子m三次方+2m²+2010的值是_______3,设a,b是方程x²+x-2010=0的两个实数根,则a²+2a+b的值是_______
2,m是方程x²+x-1=0的根,则式子m三次方+2m²+2010的值是_______3,设a,b是方程x²+x-2010=0的两个实数根,则a²+2a+b的值是_______
2,m是方程x²+x-1=0的根,则式子m三次方+2m²+2010的值是_______3,设a,b是方程x²+x-2010=0的两个实数根,则a²+2a+b的值是_______
解
m是方程x²+x-1=0的解
∴m²+m-1=0
即m²+m=1
∴m³+2m²+2010
=m(m²+m)+m²+2010
=m×1+m²+2010
=m²+m+2010
=1+2010
=2011
a,b是方程x²+x-2010=0的解
由韦达定理得:
a+b=-1
又a²+a-2010=0
∴a²+a=2010
∴a²+2a+b
=(a²+a)+(a+b)
=2010+(-1)
=2009