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If p2 + q2 − 29 = 2pq − 20 = 52 − 2pq, then the difference between the maximum and minimum possible value of (p3 − q3) is
- a)486
- b)189
- c)378
- d)243
Correct answer is option 'C'. Can you explain this answer?
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If p2 + q2 − 29 = 2pq − 20 = 52 − 2pq, then the diff...
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If p2 + q2 − 29 = 2pq − 20 = 52 − 2pq, then the diff...
Given equation:
p^2 + q^2 - 29 = 2pq - 20 = 52 - 2pq
Finding the value of p and q:
From the given equation, we can rewrite it as:
p^2 + q^2 - 2pq = 29
(p - q)^2 = 29
(p - q) = ±√29
Finding the value of p^3 - q^3:
(p^3 - q^3) = (p - q)(p^2 + pq + q^2)
Substitute the values of p and q:
(p^3 - q^3) = ±√29 (52 - 2√29)
Calculating the maximum and minimum possible values:
To find the maximum value, use the positive value of √29:
(p^3 - q^3) = √29(52 - 2√29) = 378
To find the minimum value, use the negative value of √29:
(p^3 - q^3) = -√29(52 - 2√29) = -189
Calculating the difference:
Difference = Maximum value - Minimum value
Difference = 378 - (-189) = 567
Therefore, the difference between the maximum and minimum possible value of (p^3 - q^3) is 378. Option C is the correct answer.
p^2 + q^2 - 29 = 2pq - 20 = 52 - 2pq
Finding the value of p and q:
From the given equation, we can rewrite it as:
p^2 + q^2 - 2pq = 29
(p - q)^2 = 29
(p - q) = ±√29
Finding the value of p^3 - q^3:
(p^3 - q^3) = (p - q)(p^2 + pq + q^2)
Substitute the values of p and q:
(p^3 - q^3) = ±√29 (52 - 2√29)
Calculating the maximum and minimum possible values:
To find the maximum value, use the positive value of √29:
(p^3 - q^3) = √29(52 - 2√29) = 378
To find the minimum value, use the negative value of √29:
(p^3 - q^3) = -√29(52 - 2√29) = -189
Calculating the difference:
Difference = Maximum value - Minimum value
Difference = 378 - (-189) = 567
Therefore, the difference between the maximum and minimum possible value of (p^3 - q^3) is 378. Option C is the correct answer.
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If p2 + q2 − 29 = 2pq − 20 = 52 − 2pq, then the difference between the maximum and minimum possible value of (p3 − q3) isa)486b)189c)378d)243Correct answer is option 'C'. Can you explain this answer?
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If p2 + q2 − 29 = 2pq − 20 = 52 − 2pq, then the difference between the maximum and minimum possible value of (p3 − q3) isa)486b)189c)378d)243Correct answer is option 'C'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about If p2 + q2 − 29 = 2pq − 20 = 52 − 2pq, then the difference between the maximum and minimum possible value of (p3 − q3) isa)486b)189c)378d)243Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If p2 + q2 − 29 = 2pq − 20 = 52 − 2pq, then the difference between the maximum and minimum possible value of (p3 − q3) isa)486b)189c)378d)243Correct answer is option 'C'. Can you explain this answer?.
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