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Question Number 136320 by radians last updated on 20/Mar/21

Answered by Olaf last updated on 20/Mar/21

coefficient x^2  is same as x^3  :  ⇒ C_2 ^(2020) a^2 b^(2018)  = C_3 ^(2020) a^3 b^(2017)   ((2020×2019)/2)b = ((2020×2019×2018)/6)a  b = ((2018)/3)a  a = 3, b = 2018

$$\mathrm{coefficient}\:{x}^{\mathrm{2}} \:\mathrm{is}\:\mathrm{same}\:\mathrm{as}\:{x}^{\mathrm{3}} \:: \\ $$$$\Rightarrow\:\mathrm{C}_{\mathrm{2}} ^{\mathrm{2020}} {a}^{\mathrm{2}} {b}^{\mathrm{2018}} \:=\:\mathrm{C}_{\mathrm{3}} ^{\mathrm{2020}} {a}^{\mathrm{3}} {b}^{\mathrm{2017}} \\ $$$$\frac{\mathrm{2020}×\mathrm{2019}}{\mathrm{2}}{b}\:=\:\frac{\mathrm{2020}×\mathrm{2019}×\mathrm{2018}}{\mathrm{6}}{a} \\ $$$${b}\:=\:\frac{\mathrm{2018}}{\mathrm{3}}{a} \\ $$$${a}\:=\:\mathrm{3},\:{b}\:=\:\mathrm{2018} \\ $$

Commented by radians last updated on 20/Mar/21

thank you so much

$${thank}\:{you}\:{so}\:{much} \\ $$

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