ax*3(x的3次方)=by*3=cz*3,且1/x+1/y+1/z=1.求證(ax*2+by*2+cz*2)*1/3=a*1/3+b*1/3+c*1/3.請回答, 這一類的題多數應該怎麼解,請說明,

ax*3(x的3次方)=by*3=cz*3,且1/x+1/y+1/z=1.求證(ax*2+by*2+cz*2)*1/3=a*1/3+b*1/3+c*1/3.請回答, 這一類的題多數應該怎麼解,請說明,

設k=ax^3=by^3=cz^3則ax^2/k=1/x,by^2/k=1/y,cz^2/k=1/z1/x+1/y+1/z=1即:ax^2+by^2+cz^2=k=ax^3=by^3=cz^3(ax^2+by^2+cz^2)^(1/3)=k^(1/3)=x*a^(1/3)=y*b^(1/3)=z*c^(1/3)a^(1/3)+b^(1/3)+c^(1/3)=k^(1/3)*(1/x+1/…