Question

Solutia ecuatiei (3-2sqrt2)^x-2(sqrt2-1)^x=3

Answer 1

$(3-2 \sqrt{2})^x-2( \sqrt{2}-1)^x=3,dar,( \sqrt{2}-1)^2=2-2 \sqrt{2}+1=3-2 \sqrt{2}$, Deci notand $(\sqrt{2}-1)^x=y,unde,y\ \textgreater \ 0$, se obtine ecuatia y²-2y-3=0 cu radacinile una =3 si a doua =-1<0, deci nu corespunde, vom avea :$(\sqrt{2}-1)^x=3,logaritmam,in,baza,10,rezulta,x= \frac{lg3}{lg( \sqrt{2}-1 )}$