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Question Number 64153 by meme last updated on 14/Jul/19

$$solveto{z}^2{x}^2-y^2=24$$

Answered by mr W last updated on 15/Jul/19

$$(x-y)(x+y)=24=a\times b=1\times 24=2\times 12=3\times 8=4\times 6$$$$x=\frac{a+b}{2}$$$$y=\frac{b-a}{2}$$$$aandbshouldbebothevenorodd,$$$$\Rightarrow a\times b=2\times 12or4\times 6$$$$\Rightarrow x=\frac{2+12}{2}=7,y=\frac{12-2}{2}=5$$$$\Rightarrow x=\frac{4+6}{2}=5,y=\frac{6-4}{2}=1$$$$$$$$\Rightarrow (x,y)=(\pm 7,\pm 5)or(\pm 5,\pm 1)$$

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