Menu Close

solve-for-x-y-gt-0-2x-y-2020-3y-x-2021-

Tinku Tara 0 Comments
Pin




Question Number 93460 by john santu last updated on 13/May/20
solve for x,y >0 2x⌊y⌋ = 2020 3y⌊x⌋ = 2021
solveforx,y>02x⌊y⌋=20203y⌊x⌋=2021
Commented by john santu last updated on 13/May/20
ans : (((1010)/(673)) , ((2021)/3))
ans:(1010673,20213)
Answered by mr W last updated on 16/May/20
⌊x⌋=n≠0 ⌊y⌋=m≠0 2020=2x⌊y⌋≥2nm ⇒nm≤1010 2020=2x⌊y⌋<2(n+1)m ⇒(n+1)m≥1011 2021=3y⌊x⌋≥3mn⇒mn≤((2021)/3)=673 2021=3y⌊x⌋<3(m+1)n⇒n(m+1)≥674 ⇒m−n≥337 m≥337+n mn=(337+n)n≤673 ⇒n=1 is the only solution ⇒y=((2021)/3) ⇒x=((1010)/(⌊((2021)/3)⌋))=((1010)/(673))
⌊x⌋=n≠0⌊y⌋=m≠02020=2x⌊y⌋⩾2nm⇒nm⩽10102020=2x⌊y⌋<2(n+1)m⇒(n+1)m⩾10112021=3y⌊x⌋⩾3mn⇒mn⩽20213=6732021=3y⌊x⌋<3(m+1)n⇒n(m+1)⩾674⇒m−n⩾337m⩾337+nmn=(337+n)n⩽673⇒n=1istheonlysolution⇒y=20213⇒x=1010⌊20213⌋=1010673

Pin

Leave a Reply

Your email address will not be published. Required fields are marked *