設x>0,y>0且x≠y求證(x^3+y^3)^(1/3)<(x^2+y^2)^(1/2)

熱心網友

(x^2+y^2)^3=x^6+y^6+3x^4y^2+3x^2y^4 (1)(x^3+y^2)^2=x^6+y^6+2x^3y^3 (2)(1)-(2)=3x^2*y^2(x-y)^2+4x^3*y^30所以(x^3+y^3)^(1/3)<(x^2+y^2)^(1/2)