根号下(r1+r3)+根号下(r2+r3)=根号下(r1+r2),求r1,r2,r3的关系

1个回答

  • 两边同时lg

    得到 lg[根号下(r1+r3)+根号下(r2+r3)]=lg[根号下(r1+r2)]

    两边乘2得到 lg[根号下(r1+r3)+根号下(r2+r3)]^2=lg(r1+r2)

    化简 lg{r1+r3+r2+r3+2*[根号下(r1+r3)*根号下(r2+r3)]}=lg(r1+r2)

    去掉lg得到 {r1+r3+r2+r3+2*[根号下(r1+r3)*根号下(r2+r3)]}=r1+r2

    化简 2*r3+2*[根号下(r1+r3)*根号下(r2+r3)]=0

    则 r3+[根号下(r1+r3)*根号下(r2+r3)]=0

    化简 r1*r2+r2*r3+r1*r3=0

    r3=-r1*r2/(r1+r2)