If sum and difference of two expressions is $5 x^{2} - x - 4$ and $x^{2} + 9 x - 10$ respectively, then the expressions are

(4 x^{2} + 8 x - 6), (4 x^{2} - 10 x + 2)

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(2 x^{2} + 4 x - 3), (3 x^{2} - 10 x - 6)

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(3 x^{2} + 4 x - 7), (2 x^{2} - 5 x + 3)

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(3 x^{2} + 4 x + 7), (2 x^{2} - 5 x - 3)

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Solution

The correct option is C $(3 x^{2} + 4 x - 7), (2 x^{2} - 5 x + 3)$
Let the two expressions are X and Y then by hypothesis
$X + Y = 5 x^{2} - x - 4$ ...(i)
and $X - Y = x^{2} + 9 x - 10$ ...(ii)

Adding and subtracting both equations we get
$2 X = 6 x^{2} + 8 x - 14$
or $X = 3 x^{2} + 4 x - 7$
and $2 Y = 4 x^{2} - 10 x + 6$
or $Y = 2 x^{2} - 5 x + 3$

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