The H.C.F. of two expressions is x and their L.C.M. is $x^{3} - 9 x$ . If one of the expression is $x^{2} + 3 x$ , then the other expression is

x^{2} - 3 x

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x^{3} - 3 x

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x^{2} + 9 x

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x^{2} - 9 x

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Solution

The correct option is A $x^{2} - 3 x$
$G i v e n H C F = x, L C M = x^{3} - 9 x, o n e n u m b e r = x^{2} + 3 x . H C F \times L C M = x (x^{3} - 9 x) = x^{4} - 9 x^{2} . L e t o n e n u m b e r b e P . ∴ P r o d u c t o f t h e n u m b e r s = P (x^{2} + 3 x) w e k n o w L C M \times H C F = P r o d u c t o f t h e n u m b e r . ∴ P (x^{2} + 3 x) = x^{4} - 9 x^{2} = (x^{2} + 3 x) (x^{2} - 3 x) ∴ P = \frac{(x^{2} + 3 x) (x^{2} - 3 x)}{x^{2} + 3 x} = x^{2} - 3 x ∴ T h e o t h e r n u m b e r i s x^{2} - 3 x .$

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Similar questions

x^{3} - 9 x

x^{2} + 3 x

x^{3} - 9 x

x^{2} + 3 x

The H.C.F. and L.C.M. of two expression are (x − 3) and (x³ − 5x² − 2x + 24) respectively. If one of the expression is (x² − 7x + 12) find the other.

(x^{2} + 6 x + 8) (x + 1)

(x + 1)

x^{2} + 3 x + 2

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(x^{3} - 5 x^{2} - 2 x + 24)

(x^{2} - 7 x + 12)

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