当x=2分之1时,f(x)的最大值为25
可以设
f(x)=a(x-1/2)^2+25
=ax^2-ax+a/4+25=0
x1+x2=1
x1x2=a/4+25
x1^3+x2^3
=(x1+x2)(x1^2-x1x2+x2^2)
=(x1+x2)((x1+x2)^2-3x1x2)
=1-3x1x2
=1-3a/4-75=19
得a=-124
f(x)=-124(x-1/2)^2+25
=-124x^2+124x-6
当x=2分之1时,f(x)的最大值为25
可以设
f(x)=a(x-1/2)^2+25
=ax^2-ax+a/4+25=0
x1+x2=1
x1x2=a/4+25
x1^3+x2^3
=(x1+x2)(x1^2-x1x2+x2^2)
=(x1+x2)((x1+x2)^2-3x1x2)
=1-3x1x2
=1-3a/4-75=19
得a=-124
f(x)=-124(x-1/2)^2+25
=-124x^2+124x-6