证明,有两个电阻R1和R2串联在电压为U的电路中

P1=i串*i串*R1 (i串=U/(R1+R2)
=U*U*R1/[(R1+R2)*(R1+R2)] ----式1
P2=U*U*R2/[(R1+R2)*(R1+R2)] ----式2
代入式1,式2则
(P1+P2)^3={U*U*R1/[(R1+R2)*(R1+R2)]+ U*U*R2/[(R1+R2)*(R1+R2)}^3
={U*U*(R1+R2)/[(R1+R2)*(R1+R2)]}^3
={U*U/(R1+R2)}^3
=U^6/[(R1+R2)^3] --- 式3
P1*P2=U*U*R1/[(R1+R2)*(R1+R2)] * U*U*R2/[(R1+R2)*(R1+R2)]
=U^4*R1*R2/[(R1+R2)^2] ---式4
(P1+P2)^3/P1P2=式3/式4
=U^6/[(R1+R2)^3]/{U^4*R1*R2/[(R1+R2)^2]}
=U^2/[R1*R2/(R1+R2)] ----式5

P并=U*U/(R1//R2)
=U*U/[R1*R2/(R1+R2)] -------式6
式5,式6相等，所以命题成立