What should be taken away from ${3 x}^{2} - {4 y}^{2} + 5 x y + 20$ to get ${- x}^{2} - y^{2} + 6 x y + 20$ .

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Solution

$3 x^{2} - 4 y^{2} + 5 x y + 20 - a$
$= - x^{2} - y^{2} + 6 x y + 20$
$\Rightarrow 3 x^{2} + x^{2} - 4 y^{2} + y^{2} + 5 x y - 6 x y = a$
$\Rightarrow 4 x^{2} - 3 y^{2} - x y = a$ .

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Question 5

What should be subtracted from $3 x^{2} - 4 y^{2} + 5 x y + 20$ to obtain $- x^{2} - y^{2} + 6 x y + 20$ ?

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