mariamikayla
Answered

At Westonci.ca, we connect you with the best answers from a community of experienced and knowledgeable individuals. Get quick and reliable solutions to your questions from a community of seasoned experts on our user-friendly platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

Solve the ecuation:

[tex]x=\frac{[x]+2012}{\{x\}+2013}[/tex]

where [x] is the whole part of the number x and {x} is the fractional part of the number x.

Sagot :

crisforp
Scrii x = [ x ] + { x } ;
Folosesti proprietatea fundamentala a proportiilor;
Apoi, exprimi [ x ] in functie de { x }, si obtii ca :
[ x ] = ( 2012 - { x } ^2 - 2013{ x } ) / ( 2012 + { x } ) ;
Fie { x } = t ∈ [ 0 , 1 ) ;
 Obtii ca [ x ] = - t - 1 + 4024 / ( t + 2012 ) ;
Stim ca [ x ] ∈ Z ;
Atunci t = 0 sau t = 2012 ;
Convine numai t = 0 => x = [ x ] ;
Ecuatia originala va avea solutia 1.

Bafta!

Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.