Question : If p + q = 12 and pq = 14, then find the value of p2 – pq + q2.
Option 1: 192
Option 2: 181
Option 3: 102
Option 4: 144
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Correct Answer: 102
Solution :
Given: $p + q = 12$ and $pq = 14$
Squaring both sides, we get,
$(p + q)^2 = 12^2$
⇒ $p^2 + 2pq + q^2=144$
⇒ $p^2 + 2\times14 + q^2=144$
⇒ $p^2 + q^2 =144- 28$
⇒ $p^2 + q^2 =116$
$\therefore p^2+q^2-pq=116-14=102$
Hence, the correct answer is 102.
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