If let us calculate the simplified value of

Formula used.

(a – b)² = a² – 2ab + b²

3x² – 5xy + 3y²

Add and subtract xy to the equation.

3x² – 5xy + 3y² [ + xy – xy]

3x² – 6xy + 3y² + xy

3[x² – 2xy + y²] + xy

3[x-y]² + xy

x = 2 + √3

y = 2 – √3

xy = (2 + √3) × ( 2-√3)

xy = (2)² – (√3)²

= 4 – 3

= 1

x – y = 2 + √3 – [2-√3]

x – y = 2√3

Putting the values we get;

3[2√3]² + 1

3[12] + 1

36 + 1 = 37