若正实数$x,y$满足$x^3+y^3=(4x-5y)y$ 则 $y$ 的最大值为____
解答:$x^3+y^3+y^2=4(x-y)yle x^2$,故$y^3+y^2=x^2-x^3=dfrac{x(2-2x)x}{2}ledfrac{4}{27}$,故由$f(t)=t^3+t^2$的单调性$yle dfrac{1}{3}$
若正实数$x,y$满足$x^3+y^3=(4x-5y)y$ 则 $y$ 的最大值为____
解答:$x^3+y^3+y^2=4(x-y)yle x^2$,故$y^3+y^2=x^2-x^3=dfrac{x(2-2x)x}{2}ledfrac{4}{27}$,故由$f(t)=t^3+t^2$的单调性$yle dfrac{1}{3}$