CAT 2023 Linear and Quadratic Equations Question (Hard)

Question

If p 2 q 2 - 29 2pq - 20 52 - 2pq, then the difference between the maximum and minimum possible values of is

Accepted Answer

Step 1 Given equations p 2 q 2 - 29 2pq - 20 52 - 2pq Step 2 Solve second equality 2pq - 20 52 - 2pq 4pq 72 Rightarrow pq 18 Step 3 Solve first equality p 2 q 2 - 29 2pq - 20 p 2 q 2 - 2pq 29 - 20 p - q 2 9 Rightarrow p - q pm 3 Step 4 Formula for difference of cubes p 3 - q 3 p - q 3 3pq p - q Step

CAT 2023

Quantitative

Linear and Quadratic Equations

Hard

If $p^2 + q^2 - 29 = 2pq - 20 = 52 - 2pq,$ then the difference between the maximum and minimum possible values of $p^3 - q^3$ is:

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