The following equation is from a force triangle from statics (mechanics) and was written by applying the law of cosines.

$F^2=F_R^2+a-bF_R$ (1)

where a and b are constants, $F_R$ is the resultant force and $F$ is a component. The question I was trying to solve tells me that the resultant force is a minimum which means $\frac{dF_R}{dF}=0$. When I implicitly differentiate the equation(1), the derivative function is also an implicit one. I know the problem can be solved using another equation which explicitly expresses $F_R$ but I wonder if eqn (1) can be expressed explicitly. My question is:

How can I leave $F_R$ alone on one side of eqn(1)?

  • $\begingroup$ $F_R$ can be expressed by it self by solving a quadratic - however, the solution for F will be 0. $\endgroup$ – Chinny84 Jun 21 '19 at 11:44
  • $\begingroup$ You are right. F turns out to be zero. That is another issue that confuses me $\endgroup$ – Ali Kıral Jun 21 '19 at 11:52

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