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Question

Find the value of $(p^{2} + q^{2} + r^{2}) (p q + q r); p = 2, q = - 3$

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Solution

Given: $(p^{2} + q^{2} + r^{2}) (p q + q r)$
Substituting $p = 2, q = - 3$ in the above equation, we get
$= (2^{2} + {(- 3)}^{2} + r^{2}) (2 \times - 3 + (- 3) r)$
$= (4 + 9 + r^{2}) (- 6 - 3 r)$
$= - (13 + r^{2}) (3 r + 6)$
$= - (39 r + 78 + 3 r^{3} + 6 r^{2})$
$= - (3 r^{3} + 6 r^{2} + 39 r + 78)$

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