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Algebraic Identities

If x-y=7 an...

Question

If $x - y = 7 a n d x^{3} - y^{3} = 133$ ; find:
the value of $x y$

A

12

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B

-4

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C

-10

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D

5

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Solution

The correct option is C -10
Let,the two number be $x$ and $y$
Therefore,we get
$x - y = 7$
$x^{3} - y^{3} = 133$
Now,
$x - y = 7$
Squaring both sides,
$=> (x - y)^{2} = 7^{2}$
$=> x^{2} + y^{2} - 2 x y = 49$
$=> x^{2} + y^{2} = 49 + 2 x y$
Now,
$x^{3} - y^{3} = 133$
$=> (x - y) (x^{2} + y^{2} + x y) = 133$
$=> 7 (49 + 2 x y + x y) = 133$
$=> 49 + 3 x y = \frac{133}{7}$
$=> 3 x y = 19 - 49$
$=> x y = \frac{- 30}{3}$
$=> x y = - 10$

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