Find the integral solution of x^2+y^2=(xy-7)^2
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Hit and Trail method is superb for this question, Because here given two variable but equation is only one .
Here given, x² + y² = (xy - 7)²
It seems like Pythagoras theorem , H² = P² + B². do you not think ? I hope you too think same theory.
now, we have to assume x , y and z in such a way that it follow above conditions.
Let use a simple Pythagoras triplet :{3, 4 , 5}
Let x = 3, y = 4
Then, LHS = x² + y² = 3² + 4² = 25
RHS = (xy - 7)² = (3 × 4 - 7)² = (5)² = 25
Hence, x = 3 and y = 4 is a solution of given equation
Also possible to assume x = 4 and y = 3
Hence, we get two solutions (3, 4) and (4,3)
For finding more solution try more Pythagoras triplets .
So, answer is x = 3, y = 4 or x = 4 , y = 3
Here given, x² + y² = (xy - 7)²
It seems like Pythagoras theorem , H² = P² + B². do you not think ? I hope you too think same theory.
now, we have to assume x , y and z in such a way that it follow above conditions.
Let use a simple Pythagoras triplet :{3, 4 , 5}
Let x = 3, y = 4
Then, LHS = x² + y² = 3² + 4² = 25
RHS = (xy - 7)² = (3 × 4 - 7)² = (5)² = 25
Hence, x = 3 and y = 4 is a solution of given equation
Also possible to assume x = 4 and y = 3
Hence, we get two solutions (3, 4) and (4,3)
For finding more solution try more Pythagoras triplets .
So, answer is x = 3, y = 4 or x = 4 , y = 3
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