# separating the dependent variable in an implicitly expressed function

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)?

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