What is the turbine inlet temperature for real gas turbine cycle when pressure ratio is 7, compressor inlet temperature is 300K and Cp/Cv=1.4 and if the turbine and the compressor efficiencies are 85% and efficiency from fuel to axial power is 38%. How much it improves if we install a recuperator with efficiency of 50%?

I solved it, but got negative inlet temperature, seems like I used right equations, but may be I got wrong the term "form fuel to axial power". I supposed that ((t3-t4)-(t2-t1))/(t3-t2)=0.38. Could someone help me because it is an exam exercise)))