Question

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Answer 1

Observi   ca  (3+2√²)*(3-2√2)=9-8=1
(3+2√2)^x(3-2√2)^x=1=>
3-2√2)^x=1/(3+2√2)
Inlocuiesti   in   ecuatie
(3+2√2)^x+1/(3+2√2)^x=2
aduci  la   acelasi  numitor
(3+2√2)^2x+1=2(3+2√2)^x
SUbstitutie
(3+2√2)^=y
y²+1=2y
y²-2y+1=0
(y-1)²=0
y=1
revii  la   substitutie
(2+2√2)^x=1=>
x=0