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
New: SSC CHSL Tier 2 answer key released | SSC CHSL 2024 Notification PDF
Recommended: How to crack SSC CHSL | SSC CHSL exam guide
Don't Miss: Month-wise Current Affairs | Upcoming government exams
Correct Answer: –3
Solution :
As we know $p^3 - q^3 = (p - q)(p^2 + pq + q^2)$
Comparing $\small p^{3}-q^{3}=\left (p-q \right )\left \{ \left (p-q \right)^{2}-xpq \right \}$ with the above identity, we get,
$p^2 + pq + q^2 = (p-q)^2-xpq$
⇒ $p^2 + pq + q^2 = p^2+q^2-2pq - xpq$
⇒ $pq = -pq(2+x)$
⇒ $2+x = -1$
⇒ $ x=-3$
Hence, the correct answer is –3.
Related Questions
Know More about
Staff Selection Commission Combined High ...
Result | Eligibility | Application | Admit Card | Answer Key | Preparation Tips | Cutoff
Get Updates Brochure
Your Staff Selection Commission Combined Higher Secondary Level Exam brochure has been successfully mailed to your registered email id “”.
