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According to the answer X,Y has the same value i.e 12
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You are right, The main reason is:
x²-8y=4x
From here,we obtain x²-4x=8y
Then x|x²-4x and we can say x|8y hence according to the question, x|y. In the same way, y|x and we obtain,x=y. Then we can solve the equation and will get x=0 and 12. But 0 is not a positive integer. So x must be 12.
Just to let you know. You can use the “√” symbol…
But, take x=20. then y=((20)^2-4(20))/8=40. here x is not equals y. both are positive integers. x is not a multiple of 8. It satisfies all the conditions. Now, take x=12. then y=((12)^2-4(12))/8=12. here x=y which violates the condition “x,y are two different positive integers”. according to me, the answer should be sqrt(20). but, i tried to answer by decimal representation, exact form, some other values of x like 36. None works. I want to know where i made a mistake.