若正实数$x,y$满足$x^3+y^3=(4x-5y)y$ 则 $y$ 的最大值为____
解答:$x^3+y^3+y^2=4(x-y)y\le x^2$,故$y^3+y^2=x^2-x^3=\dfrac{x(2-2x)x}{2}\le\dfrac{4}{27}$,故由$f(t)=t^3+t^2$的单调性$y\le \dfrac{1}{3}$
标签：le,5y,4x,2x,27,331,MT,齐次,dfrac
来源： https://www.cnblogs.com/mathstudy/p/10755678.html