Add $p (p - q), q (q - r)$ and $r (r - p)$

p^{3} + q^{2} + r^{2} - p q + q r - p r

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p^{2} + 2 q^{2} + r^{2} - p q - q r + p r

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p^{2} + q^{2} + r^{2} - p q - q r - p r

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p^{3} + q^{2} + r^{2} - p q - q r - p r

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Solution

The correct option is D $p^{2} + q^{2} + r^{2} - p q - q r - p r$
given, $p (p - q) + q (q - r) + r (r - p)$
$= (p \times p - p \times q) + (q \times q - q \times r) + (r \times r - r \times p)$
$= p^{2} - p q + q^{2} - q r + r^{2} - p r$
$= p^{2} + q^{2} + r^{2} - p q - q r - p r$

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Question 9

In $Δ P Q R$ ,

a) PQ - QR > PR
b) PQ + QR < PR
c) PQ - QR < PR
d) PQ + PR < QR

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