设x₁,x₂是方程x²-x-2014=0的两实数根,求x³₁+2015x₂-2014的值
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![设x₁,x₂是方程x²-x-2014=0的两实数根,求x³₁+2015x₂-2014的值](/uploads/image/z/2537163-27-3.jpg?t=%E8%AE%BEx%26%238321%3B%2Cx%26%238322%3B%E6%98%AF%E6%96%B9%E7%A8%8Bx%26%23178%3B-x-2014%3D0%E7%9A%84%E4%B8%A4%E5%AE%9E%E6%95%B0%E6%A0%B9%2C%E6%B1%82x%26%23179%3B%26%238321%3B%2B2015x%26%238322%3B-2014%E7%9A%84%E5%80%BC)
设x₁,x₂是方程x²-x-2014=0的两实数根,求x³₁+2015x₂-2014的值
设x₁,x₂是方程x²-x-2014=0的两实数根,求x³₁+2015x₂-2014的值
设x₁,x₂是方程x²-x-2014=0的两实数根,求x³₁+2015x₂-2014的值
x₁,x₂是方程x²-x-2014=0的两实数根,则
x₁+x₂=1 x₁x₂=-2004
x₁²-x₁-2014=0 x₁²=x₁+2014
于是
x³₁+2015x₂-2014
=(x₁+2014)x₁+2015x₂-2014
=x₁²+2014x₁+2015x₂-2014
=x₁+2014+2014x₁+2015x₂-2014
=2015(x₁+x₂)
=2015