Thank you for explaining. x=66, y=1 is another solution. If 33^(1/16) is admitted, irrational numbers are OK. If so, x=√69, y=4 can be one of the solutions.
There are as many solutions as there are positive real numbers. If y>0 then (x,y)=(exp([y+log(65)]/√y,) y) is a solution. There are integer solutions, which are not shown in the clip: (-3, 16), (66,1). One of the integer solutions gets lost around @7:16, when the author concludes x=3 from x^2=3^2. This is a popular mistake.
You first define the domain of x and y. it should be positive integers. at 2:42 I understand b = √y is integer, but how can you guarantee a = x^(√y/2) is integer? if x is not power of 2 and √y is odd , a is irrational. in that case there are infinitely many combinations of (a+b)x(a-b).
Thank you for explaining. x=66, y=1 is another solution.
If 33^(1/16) is admitted, irrational numbers are OK. If so, x=√69, y=4 can be one of the solutions.
You are welcome! ❤
There are as many solutions as there are positive real numbers. If y>0 then
(x,y)=(exp([y+log(65)]/√y,) y) is a solution.
There are integer solutions, which are not shown in the clip: (-3, 16), (66,1).
One of the integer solutions gets lost around @7:16, when the author concludes x=3 from x^2=3^2. This is a popular mistake.
You are right! ❤
X=66 and Y=1 also balances the equation and hence a valid solution...why these numbers never figured in your solution? Any reason?
You are right! I forgot to include that in solution ❤
x = 3 & y = 16
You are right! ❤
Ответ не верный
По крайней мере х=66, у=1 тоже решение, а его нет как решения.
Да, ты прав! ❤
Obviously, wrong decision
Please identify the reason. ❤
I appreciate all your calculations but it was obvious at a glance that x=3, y=16, nevertheless we appreciate your method.
@@mauriziograndi1750 Thanks a lot ❤❤
You first define the domain of x and y. it should be positive integers.
at 2:42 I understand b = √y is integer, but how can you guarantee a = x^(√y/2) is integer?
if x is not power of 2 and √y is odd , a is irrational.
in that case there are infinitely many combinations of (a+b)x(a-b).
Thanks for your feedback! ❤