Question

Find x^2y^2/4 if x and y are integers such that y2-30x2=517-3x2y2

Answer 1

Answer:

i am not getting your question please write in

$x {}^{2} y { }^{2} \div4$

like this

Answer 2

Answer:

The value of  $\frac{x^2y^2}{4}$ = 49

Step-by-step explanation:

Given expression is, $y^2-30x^2 = 517-3x^2y^2$

                                 $y^2-30x^2+3x^2y^2 = 517$

 Rearranging the terms, $3x^2y^2+y^2-30x^2 = 517$

 By subtracting 10 on both sides, $3x^2y^2+y^2-30x^2 -10 = 517 - 10$

                                                        $y^2(3x^2+1) - 10(3x^2+1) = 507$

                                                       $(y^2-10)(3x^2+1) = 507$

            [By factorizing, 507 = 3 × 169 = 3 × 13 × 13 = 3 × 13²]

From above equation, $(y^2-10)(3x^2+1) = 3\times13\times13$

As x and y are integers, so (3x² + 1) ≠ 169 and (3x² + 1) ≠ 3

                                        (3x² + 1) = 13

                                        3x² = 13 - 1 = 12

                                          x² = 4     and   x = +2 or -2

Then y² - 10 = 3 × 13 = 39

         y² = 39 + 10 = 49

        y² = 49  and y = +7 or -7

• The value of  $\frac{x^2y^2}{4}$ = $\frac{4\times49}{4}$ = 49

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