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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Question : If p + q = 7 and p2 + q2 = 25, then find the value of pq.
Option 1: 24
Option 2: 12
Option 3: 18
Option 4: 36
Question : If a + b + c = 1, ab + bc + ca = –1, and abc = –1, then what is the value of a3 + b3 + c3?
Option 1: 1
Option 2: 5
Option 3: 3
Option 4: 2
Question : If A + B = – 5 and AB = 6, then find the value of A3 + B3.
Option 1: 35
Option 2: 45
Option 3: –35
Option 4: 215
Question : If $\small p^{3}-q^{3}=\left (p-q \right )\left \{ \left (p-q \right)^{2}-xpq \right \}$, then find the value of $x$.
Option 1: 3
Option 2: –3
Option 3: 1
Option 4: –1
Question : If a + b + c = 0, then the value of (a + b – c)2 + ( b + c – a)2 + ( c + a – b)2 is:
Option 1: 0
Option 2: 8abc
Option 3: 4(a2 + b2 + c2)
Option 4: 4(ab + bc + ca)
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