Menu Close

3y-2x-7-0-x-2-4y-2-21-0-




Question Number 26625 by Leong last updated on 27/Dec/17
3y−2x+7=0  x^2 −4y^2 −21=0
$$\mathrm{3y}−\mathrm{2x}+\mathrm{7}=\mathrm{0} \\ $$$$\mathrm{x}^{\mathrm{2}} −\mathrm{4y}^{\mathrm{2}} −\mathrm{21}=\mathrm{0} \\ $$
Answered by ajfour last updated on 27/Dec/17
(x−2y)(x+2y)=21  (2x−4y)(2x+4y)=84  (3y+7−4y)(3y+7+4y)=84  (7−y)(y+1)=12  y=5,1  for y=5, x=11  for y=1, x=5  hence (5,1)  and (11,5) .
$$\left({x}−\mathrm{2}{y}\right)\left({x}+\mathrm{2}{y}\right)=\mathrm{21} \\ $$$$\left(\mathrm{2}{x}−\mathrm{4}{y}\right)\left(\mathrm{2}{x}+\mathrm{4}{y}\right)=\mathrm{84} \\ $$$$\left(\mathrm{3}{y}+\mathrm{7}−\mathrm{4}{y}\right)\left(\mathrm{3}{y}+\mathrm{7}+\mathrm{4}{y}\right)=\mathrm{84} \\ $$$$\left(\mathrm{7}−{y}\right)\left({y}+\mathrm{1}\right)=\mathrm{12} \\ $$$${y}=\mathrm{5},\mathrm{1} \\ $$$${for}\:{y}=\mathrm{5},\:{x}=\mathrm{11} \\ $$$${for}\:{y}=\mathrm{1},\:{x}=\mathrm{5} \\ $$$${hence}\:\left(\mathrm{5},\mathrm{1}\right)\:\:{and}\:\left(\mathrm{11},\mathrm{5}\right)\:. \\ $$

Leave a Reply

Your email address will not be published.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