Question

Rezolvati ecuatia : 3^x+4^x=8-x; x apartine R.

Answer 1

$\displaystyle Fie~f,g: \mathbb{R} \to \mathbb{R},~f(x)=3^x+4^x~si~g(x)=8-x. \\ \\ Observam~ca~f~este~strict~crescatoare,~iar~g~este~strict \\ \\ descrescatoare. \\ \\ Prin~urmare~ecuatia~f(x)=g(x)~admite~cel~mult~o~solutie, \\ \\ si~cum~x=1~este~solutie,~aceasta~este~unica~solutie~a~ecuatiei \\ \\ date.$