SOLUTION: a) If 729^x = 3 and x^y = 216 find xy b) If x - 5√x - 1 = 0 find x² + 1/x²

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: a) If 729^x = 3 and x^y = 216 find xy b) If x - 5√x - 1 = 0 find x² + 1/x²       Log On


   

Question 1209761: a) If 729^x = 3
and x^y = 216
find xy
b) If x - 5√x - 1 = 0
find x² + 1/x²

Answer by ikleyn(52747) About Me  (Show Source):
You can put this solution on YOUR website!
.

Here I will solve part (a). 

Notice that 729 = 3^6;  Therefore, equation  729%5Ex = 3  has a unique solution x = 1/6.


Hence, the second equation  x%5Ey = 216  is  %281%2F6%29%5Ey = 6%5E3.


It has a unique solution  y = -3.


Thus, xy = %281%2F6%29%2A3 = 1%2F2.   Answer to problem (a)

Part (a) is solved.