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Solve the Following Question and Mark the Best Possible Option. Find 3x2y2 If X and Y Are Integers Such that Y2 + 3x2y2 = 30x2 + 517. - Mathematics

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MCQ

Solve the following question and mark the best possible option.
Find 3x2y2 if x and y are integers such that y2 + 3x2y2 = 30x2 + 517.

Options

  • 612

  • 418

  • 588

  • None of these

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Solution

If we move the x2 term to the left side, it is factorable:
(3x2 + 1) (y2 – 10) = 517 – 10 = 507 is equal to 3 x 132.
Since x and y are integers, 3x2 + 1 cannot equal a multiple of 3.
169 doesn't work either, so 3x2 + 1 = 13, and x = ± 2.
This leaves y2 – 10 = 39, so y = ± 7.
Thus, 3x2y2 = 3 x 4 x 49 = 588.

Concept: Number System (Entrance Exam)
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