CAT 2023 Slot 2 QA Question 21

Multiple choice (+3 / −1) · Algebra · Identities · Try it, then check the answer and solution below.

CAT 2023 Slot 2QAAlgebra • IdentitiesModerate

p^{2}+ q^{2} - 29=2 p q-20=52-2 p q , then the difference between the maximum and minimum possible value of \left(p^{3}-q^{3}\right)

⌨️ Shortcuts:[1-4 / A-D] Select[Enter] Check[B] Star[S] Solution

Official Convenor Answer Key: B

Answer and solution

Answer: B) $378$

📌 Core Concept & Formula

We are given the equation

p^{2} + q^{2} - 29 = 2pq - 20 = 52 - 2pq

. By setting each expression equal to a common variable

k , we derive the values of

and

p^{2} + q^{2}

. Using these, we factor

p^{3} - q^{3}

and find the maximum and minimum values of

p - q$.

🔢 Step-by-

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