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Question Number 149568 by mathdanisur last updated on 06/Aug/21
solve the equation: 20z[z] - 21{z} = 2021 where {∗} is GIF and {z} = z - [z]
solvetheequation:20z[z]−21{z}=2021where{∗}isGIFand{z}=z−[z]
Answered by Olaf_Thorendsen last updated on 06/Aug/21
20z[z]−21{z} = 2021 (1) 20([z]+{z})[z]−21{z} = 2021 Let n = [z] and q = {z} (0≤q<1} 20n^2 +20qn−21q = 2021 q = ((2021−20n^2 )/(20n−21)) (2) By plotting q against n, we verify that 0≤q<1 for n = 10 only • if [z] = 10 (2) : {z} = ((2021−20×100)/(200−21)) = ((21)/(179)) ⇒ z = [x]+{z} = 10+((21)/(179)) = ((1811)/(179)) We verify in (1) that : 20.((1811)/(179)).10−21.((21)/(179)) = 2021 z = ((1811)/(179))
20z[z]−21{z}=2021(1)20([z]+{z})[z]−21{z}=2021Letn=[z]andq={z}(0⩽q<1}20n2+20qn−21q=2021q=2021−20n220n−21(2)Byplottingqagainstn,weverifythat0⩽q<1forn=10only∙if[z]=10(2):{z}=2021−20×100200−21=21179⇒z=[x]+{z}=10+21179=1811179Weverifyin(1)that:20.1811179.10−21.21179=2021z=1811179
Commented by mathdanisur last updated on 07/Aug/21
Ser, thank you cool
Ser,thankyoucool

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