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Adjoint of a Matrix

Find the valu...

Question

Find the value of pq if $p^{3} - q^{3} = 68$ and p - q = -4

A

1

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B

23

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C

- 11

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D

32

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Solution

The correct option is B $- 11$
We know , $(p - q)^{3} = p^{3} - q^{3} - 3 p q (p - q)$
$\Rightarrow 3 p q (p - q) = p^{3} - q^{3} - (p - q)^{3}$
$\Rightarrow 3 p q (- 4) = 68 - (- 4)^{3}$
$\Rightarrow - 12 p q = 68 - (- 64) = 68 + 64 = 132$
$\Rightarrow p q = \frac{132}{- 12} = - 11$

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