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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