Показательное неравенство

  • 25\3*2^{sqrt{x-1}}+8*2^{-sqrt{x-1}}-25>0........(sqrt{x-1} to t)\3*2^t-25+8*2^{-t}>0\2^{-t}(3*2^{2t}-25*2^t+8)>0 .......(2^{-t}>0)\3*2^{2t}-25*2^t+8>0\D=25^2-4*3*8 = 625-96=529=23^2\ left { {{0<2^t8}} right\ left { {{t<-log_23<0} atop {t>3}} right\sqrt{x-1}>3\x-1>9\x>10' alt='3*2^{sqrt{x-1}}+2^{3-sqrt{x-1}}>25\3*2^{sqrt{x-1}}+8*2^{-sqrt{x-1}}-25>0........(sqrt{x-1} to t)\3*2^t-25+8*2^{-t}>0\2^{-t}(3*2^{2t}-25*2^t+8)>0 .......(2^{-t}>0)\3*2^{2t}-25*2^t+8>0\D=25^2-4*3*8 = 625-96=529=23^2\ left { {{0<2^t8}} right\ left { {{t<-log_23<0} atop {t>3}} right\sqrt{x-1}>3\x-1>9\x>10' align='absmiddle' class='latex-formula'>