已知正实数a,b,c满足a^2+b^2+c^2=1,求ab+ac+3√2/2bc的最大值

问题描述:

已知正实数a,b,c满足a^2+b^2+c^2=1,求ab+ac+3√2/2bc的最大值

题目不明确.是3√2/(2bc)还是(3√2/2)bc?是(3√2/2)bc设b=√(1-a²)sinβ,c=√(1-a²)cosβ,∵a,b,c>0∴00内单调递增,∴g|max=g(√[2(1-a²)])=a√[2(1-a²)]+(3√2/4)*2(1-a²)-(3√2/4)*(1-a²)=a√[2(1-a²)]+(3√2/4)*(1-a²),此时,x=√[2(1-a²)],sin(β+π/4)=1,∵0