What must be subtracted from $3 x^{2} + 4 y^{2} - 5$ to get $2 x^{2} - 3 y^{2} + 5$ ?

x^{2} + 3 y^{2} + 5

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x^{2} - 4 y^{2} + 5

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x^{2} + 7 y^{2} - 10

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x^{2} - 7 y^{2} - 10

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Solution

The correct option is C $x^{2} + 7 y^{2} - 10$
$(3 x^{2} + 4 y^{2} - 5) - a = (2 x^{2} - 3 y^{2} + 5)$
$∴$ $a = 3 x^{2} + 4 y^{2} - 5 - (2 x^{2} - 3 y^{2} + 5)$
$∴$ $a = 3 x^{2} + 4 y^{2} - 5 - 2 x^{2} + 3 y^{2} - 5$
$∴$ $a = x^{2} + 7 y^{2} - 10$

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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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