# Q. 4.     (a) What should be added to $x^{2}+xy+y^{2}$ to obtain $2x^{2}+3xy?$

Let the term be a which must be added to x2 + xy + y2 to obtain 2x2 + 3xy

$\\a + x^2 + xy + y^2 = 2x^2 + 3xy \\a = 2x^2 + 3xy - (x^2 + xy + y^2) \\a = (2-1)x^2 + (3 - 1)xy -y^2 \\a = x^2 + 2xy - y^2$

x2 + 2xy - yshould be added to x2 + xy + y2 to obtain 2x2 + 3xy

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