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第九届“希望杯”全国数学竞赛中有这样一道试题 :设α ,β分别为方程ｌｏｇ2 ｘ +ｘ - 3=0和 2 ｘ+ｘ -3=0的根 ,则α +β =.现解答如下 .解法 1 (观察法 )显见 1为后一方程的一根 ,又ｆ(ｘ) =2 ｘ+ｘ - 3是增函数 ,则 1为后一方程的唯一实根 ,即 β =1.类似得α =2 ,则α +
In the Ninth “Hope Cup” national math competition, there is such a test: Let α and β be the roots of the equations log2 x +x - 3 = 0 and 2 x + x -3 = 0, then α + β =. The solution is as follows. Solution 1 (Observation method) Obviously see that 1 is one of the latter equation, and f(x) = 2 x+x - 3 is an increasing function, then 1 is the only real root of the latter equation, that is, β = 1 Similar to α = 2, then α +