a circuit with the unknown X (pure reactance) in sereis with a two parallel impedance.Z1= 4-j8 ; Z2= 1+j10 ....and total power factor is 0.707..

 

a circuit with the unknown X (pure reactance) in sereis with a two parallel impedance.Z1= 4-j8 ; Z2= 1+j10 ....and total power factor is 0.707..

Sounds more like a statement than a question, but I'll assume it's a question and see that you want to find X.

The first step is to combine the known parallel impedances into one effective impedance Zeff=Reff+jXeff. Then ask what impedances Zt=Reff+Xt can give a power factor of 0.707. Remember that series impedances add and the real and imaginary parts of the impedance are separable and distinct. The unknown X will be Xt-Xeff.

Try this approach and if you still don't get it, at least post your attempt, which is a rule here. I've already given more information than I should without you posting an attempt, or at least a statement of what you do and don't understand about this problem.