Monday, February 19, 2024

Find 3x2y2 if x and y are integers such that y2 + 3x2y2 = 30x2 + 517.

Find 3x2y2 if x and y are integers such that y2 + 3x2y2 = 30x2 + 517.

Answer.

y2 + 3x2y2 - 30x2 – 517 = 0

3x2(y2-10) + 1(y2-10) + 10 – 517 = 0

(3x2+1)(y2-10) = 507

(3x2+1)(y2-10) = 3*13*13

To x and y be integers,

3x2+1 = 13 and y2-10 = 39

3x2 = 12 and y2 = 49

x2 = 4  and y2 = 49

To find 3x2y2 we will substitute the value of x2 and y2. 3*4*49 = 588.

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