Question

ax*3(x的3次方）=by*3=cz*3,且1/x+1/y+1/z=1.求证（ax*2+by*2+cz*2)*1/3=

Answer 1

设k=ax^3=by^3=cz^3

则 ax^2/k=1/x,by^2/k=1/y,cz^2/k=1/z

1/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/y+1/z)

=k^(1/3)

所以：(ax^2+by^2+cz^2)^(1/3)=a^(1/3)+b^(1/3)+c^(1/3）