Menu Close

Question-18365




Question Number 18365 by aplus last updated on 19/Jul/17
Answered by mrW1 last updated on 19/Jul/17
x=6  y=2
$$\mathrm{x}=\mathrm{6} \\ $$$$\mathrm{y}=\mathrm{2} \\ $$
Commented by mrW1 last updated on 19/Jul/17
try & error  try with x=6 in (ii) you get y=2  check in (i)  (6x^y )^2 =(6×6^2 )^2 =6^2 ×6^4 =6^6 =x^x   ⇒x=6 and y=2 ok!  such equations don′t make much sense.  there are no general solution methods.
$$\mathrm{try}\:\&\:\mathrm{error} \\ $$$$\mathrm{try}\:\mathrm{with}\:\mathrm{x}=\mathrm{6}\:\mathrm{in}\:\left(\mathrm{ii}\right)\:\mathrm{you}\:\mathrm{get}\:\mathrm{y}=\mathrm{2} \\ $$$$\mathrm{check}\:\mathrm{in}\:\left(\mathrm{i}\right) \\ $$$$\left(\mathrm{6x}^{\mathrm{y}} \right)^{\mathrm{2}} =\left(\mathrm{6}×\mathrm{6}^{\mathrm{2}} \right)^{\mathrm{2}} =\mathrm{6}^{\mathrm{2}} ×\mathrm{6}^{\mathrm{4}} =\mathrm{6}^{\mathrm{6}} =\mathrm{x}^{\mathrm{x}} \\ $$$$\Rightarrow\mathrm{x}=\mathrm{6}\:\mathrm{and}\:\mathrm{y}=\mathrm{2}\:\mathrm{ok}! \\ $$$$\mathrm{such}\:\mathrm{equations}\:\mathrm{don}'\mathrm{t}\:\mathrm{make}\:\mathrm{much}\:\mathrm{sense}. \\ $$$$\mathrm{there}\:\mathrm{are}\:\mathrm{no}\:\mathrm{general}\:\mathrm{solution}\:\mathrm{methods}. \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *