已知實(shí)數(shù)a，b分別滿足a3-3a2+5a=1，b3-3b2+5b=5，則a+b的值為_．
已知實(shí)數(shù)a，b分別滿足a3-3a2+5a=1，b3-3b2+5b=5，則a+b的值為______．
數(shù)學(xué)人氣：485 ℃時(shí)間：2020-04-03 01:28:13
優(yōu)質(zhì)解答
由于已知的兩個(gè)等式結(jié)構(gòu)相似，因此可考慮構(gòu)造函數(shù)．將已知等式變形為（a-1）3+2（a-1）=-2，（b-1）3+2（b-1）=2，構(gòu)造函數(shù)f（x）=x3+2x，∵f（-x）=-f（x），∴f（x）是奇函數(shù)∵f′（x）=3x2+2＞0∴f（x）單調(diào)遞增...
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