Question

sa se rezolve in multimea numerelor reale ecuatia (3+2√2)^x=(1+√2)^2

Answer 1

(3+2√2)^x=1+2√2+2

(3+2√2)^x=3+2√2
(3+2√2)^x=(3+2√2)^1
x=1
as simple as that!

Answer 2

   
[tex]\displaystyle\\ (3+2 \sqrt{2} )^x=(1+\sqrt{2} )^2\\\\ (3+2 \sqrt{2} )^x=1^2+2\times 1 \times \sqrt{2}+ (\sqrt{2})^2\\\\ (3+2 \sqrt{2} )^x=1+2\sqrt{2}+ 2\\\\ (3+2 \sqrt{2} )^x=3+2\sqrt{2}\\\\ (3+2 \sqrt{2} )^x=(3+2\sqrt{2})^1 \\\\ \boxed{\bf x = 1} [/tex]