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Question Number 95966 by i jagooll last updated on 29/May/20

find all pairs of integer for xy+3x−4y = 29

$$\mathrm{find}\:\mathrm{all}\:\mathrm{pairs}\:\mathrm{of}\:\mathrm{integer}\:\mathrm{for}\: \\ $$$$\mathrm{xy}+\mathrm{3x}−\mathrm{4y}\:=\:\mathrm{29}\: \\ $$

Answered by john santu last updated on 29/May/20

⇒3x+xy−4y−12 = 17 3(x−4)+y(x−4) = 17 (x−4)(y+3) = 17 (i) for x−4=1 ⇒y+3 = 17 (5,14) (ii) for x−4=−1⇒y+3=−17 (3,−20) (iii) for x−3 = 17 ⇒y+3 = 1 (20,−2) (iv)for x−3=−17⇒y+3=−1 (−14, −4)

$$\Rightarrow\mathrm{3}{x}+{xy}−\mathrm{4}{y}−\mathrm{12}\:=\:\mathrm{17}\: \\ $$$$\mathrm{3}\left({x}−\mathrm{4}\right)+{y}\left({x}−\mathrm{4}\right)\:=\:\mathrm{17}\: \\ $$$$\left({x}−\mathrm{4}\right)\left({y}+\mathrm{3}\right)\:=\:\mathrm{17}\: \\ $$$$\left({i}\right)\:{for}\:{x}−\mathrm{4}=\mathrm{1}\:\Rightarrow{y}+\mathrm{3}\:=\:\mathrm{17}\: \\ $$$$\left(\mathrm{5},\mathrm{14}\right) \\ $$$$\left({ii}\right)\:{for}\:{x}−\mathrm{4}=−\mathrm{1}\Rightarrow\mathrm{y}+\mathrm{3}=−\mathrm{17} \\ $$$$\left(\mathrm{3},−\mathrm{20}\right) \\ $$$$\left({iii}\right)\:{for}\:{x}−\mathrm{3}\:=\:\mathrm{17}\:\Rightarrow\mathrm{y}+\mathrm{3}\:=\:\mathrm{1} \\ $$$$\left(\mathrm{20},−\mathrm{2}\right) \\ $$$$\left({iv}\right){for}\:{x}−\mathrm{3}=−\mathrm{17}\Rightarrow\mathrm{y}+\mathrm{3}=−\mathrm{1} \\ $$$$\left(−\mathrm{14},\:−\mathrm{4}\right)\: \\ $$

Commented by i jagooll last updated on 29/May/20

thank you

$$\mathrm{thank}\:\mathrm{you} \\ $$

Commented by Rasheed.Sindhi last updated on 29/May/20

Cooool!

$$\mathcal{C}{ooool}! \\ $$

Commented by john santu last updated on 29/May/20

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Commented by mr W last updated on 29/May/20

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