... EMBED Equation.3 EMBED Equation.3 EMBED Equation.3 fx este strict crescatoare pe Rgx este strict descrescatoare pe RO3 Fie a EMBED Equation.3 R. Sa se rezolve in R ecuatia EMBED Equation.3 Rezolvare EMBED Equation.3 O4 Sa se rezolve sistemul EMBED Equation.3 RezolvareConditii de existenta x,y EMBED Equation.3 RObservam ca EMBED Equation.3 este solutie a sistemuluiVerificare EMBED Equation.3 33-2227-423Cazul 1 x EMBED Equation.3 03 EMBED Equation.3 Din relatiile 1 si 2!contradictie!nu exista solutii pentru x EMBED Equation.3 03 3Cazul 2 x EMBED Equation.3 3 EMBED Equation.3 Din relatiile 1 si 2!contradictie!nu exista solutii pentru x EMBED Equation.3 3 4Din relatiile 3 si 4!ecuatia are solutie unica EMBED Equation.3 O5 Sa se rezolve ecuatia4x9x25x6x10x15xRaspunsObservam ca x0 verifica ecuatia.Verificare 111111!33 ASolutia 1 Notam 2xa3xb5xcecuatia 4x9x25x6x10x15x se poate scrie a2b2c2abacbca2b2e2aba2c2e2bcb2c2e2ac 2a2b2c2 e2abbcac! a2b2c2 eabbcacEgalitatea are loc daca abc ! 3x2x5x!x0Solutia 24x9x-6x 10x15x-25x D 10x EMBED Equation.3 Definim urmatoarele functii EMBED Equation.3 fx EMBED Equation.3 este strict descrescatoare pe R gx EMBED Equation.3 este strict crescatoare pe R O6 Sa se rezolve ecuatia EMBED Equation.3 RezolvareObservam ca x2 este solutie a ecuatiei.Verificare EMBED Equation.3 Definim urmatoarele functii EMBED Equation.3 fx EMBED Equation.3 , EMBED Equation.3 !fx este strict descrescatoare pe R gxsin EMBED Equation.3 x, EMBED Equation.3 !gx este strict crescatoare pe Rfxgx EMBED Equation.3 este strict descrescatoare pe R Deci x2 este solutie unica. O7 Sa se rezolve ecuatia EMBED Equation.3 RezolvareObservam ca x5 este solutie a ecuatiei.Verificare 301!11 ADefinim functiile fR!R, fx EMBED Equation.3 este strict crescatoare pe RgR!R, gx EMBED Equation.3 este strict descrescatoare pe Rfx EMBED Equation.3 x1x2!x1-5x2-5! EMBED Equation.3 fx1fx2!functia este strict crescatoaregx EMBED Equation.3 x1x2! x1-4x2-4! EMBED Equation.3 gx1gx2!functia este strict descrescatoare Deci x5 este solutie unica.N1 Sa se rezolve inecuatiile EMBED Equation.3 RezolvareConditii de existenta x22x0!xx20x -2 0xx-2 0- - - - - - 0 Ecuatia atasata xx20! EMBED Equation.3 Deci x EMBED Equation.3 --2 EMBED Equation.3 0 . EMBED Equation.3 Ecuatia atasata x22x-10! EMBED Equation.3 448.x -1- EMBED Equation.3 -1 EMBED Equation.3 x22x-1 0 - - - - - - - 0 EMBED Equation.3 Deci x EMBED Equation.3 -1- EMBED Equation.3 -1 EMBED Equation.3 Deci x EMBED Equation.3 -1- EMBED Equation.3 -2.c EMBED Equation.3 RezolvareConditii de existenta EMBED Equation.3 caz 1 x1! EMBED Equation.3 Ecuatia atasata EMBED Equation.3 EMBED Equation.3 4-4450!inecuatia nu are solutiicaz 2 x EMBED Equation.3 01! EMBED Equation.3 Deci inecuatia nu are solutii. A1 Sa se arate ca expresia EMBED Equation.3 este independenta de valorile strict mai mari ca 1 ale variabilelor x,y,z.Rezolvare EMBED Equation.3 ! EMBED Equation.3 !Notam EMBED Equation.3 ! E este independenta de valorile x,y,z1. x0 este solutie unica a ecuatieiSolutia unica este x0-1- EMBED Equation.3 -2-1 EMBED Equation.3 0...
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