Solve in positive integers:
$7 x^{2} - 2 x y + 3 y^{2} = 27$ .

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Solution

$7 x^{2} - 3 x y + 3 y^{2} = 27$
if we put the value of $x = 2$

$28 - 4 y + 1 =$

$3 y^{2} - 3 y - y + 1 = 0$

$3 y (y - 1) - 1 (y - 1) = 0$

$(y - 1) (3 y - 1) = 0$

$y = 1, \frac{1}{3}$

solution $x = 2, y = 1$

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Solve in positive integers:7x2−2xy+3y2=27.

7x2−3xy+3y2=27if we put the value of x=228−4y+1=3y2−3y−y+1=03y(y−1)−1(y−1)=0(y−1)(3y−1)=0y=1,13solution x=2,y=1

Solve in positive integers:
$7 x^{2} - 2 x y + 3 y^{2} = 27$ .

$7 x^{2} - 3 x y + 3 y^{2} = 27$
if we put the value of $x = 2$

$28 - 4 y + 1 =$

$3 y^{2} - 3 y - y + 1 = 0$

$3 y (y - 1) - 1 (y - 1) = 0$

$(y - 1) (3 y - 1) = 0$

$y = 1, \frac{1}{3}$

solution $x = 2, y = 1$