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If a, b, c, d and p are distinct real numbers such that (a² + b²+c²) p²-2p (ab+bc+cd) + (b²+c² + d²) ≤0, then a, b, c, d are in
(a) AP
(b) GP
(c) HP
(d) ab = cd
very short method by value put?
Most Upvoted Answer
If a, b, c, d and p are distinct real numbers such that (a² + b²+c²) p...
Given Inequality:
The given inequality is: (a² + b² + c²) p² - 2p (ab + bc + cd) + (b² + c² + d²) ≤ 0

Using Value Put Method:
Let's try to find a suitable set of values for a, b, c, d, and p that satisfy the given inequality.
- Let's assume a = 1, b = 2, c = 3, d = 4, and p = 1.
Substitute these values into the inequality:
(1² + 2² + 3²) 1² - 2(1)(2 + 2)(3 + 3)(4) + (2² + 3² + 4²)
= (1 + 4 + 9) - 2(2)(5)(4) + (4 + 9 + 16)
= 14 - 2(40) + 29
= 14 - 80 + 29
= -37
Since -37 is less than or equal to 0, the values a = 1, b = 2, c = 3, d = 4, and p = 1 satisfy the given inequality.

Conclusion:
Therefore, a, b, c, d are in (c) HP (Harmonic Progression) as they satisfy the given inequality.
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If a, b, c, d and p are distinct real numbers such that (a² + b²+c²) p²-2p (ab+bc+cd) + (b²+c² + d²) ≤0, then a, b, c, d are in(a) AP(b) GP(c) HP(d) ab = cdvery short method by value put?
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If a, b, c, d and p are distinct real numbers such that (a² + b²+c²) p²-2p (ab+bc+cd) + (b²+c² + d²) ≤0, then a, b, c, d are in(a) AP(b) GP(c) HP(d) ab = cdvery short method by value put? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If a, b, c, d and p are distinct real numbers such that (a² + b²+c²) p²-2p (ab+bc+cd) + (b²+c² + d²) ≤0, then a, b, c, d are in(a) AP(b) GP(c) HP(d) ab = cdvery short method by value put? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a, b, c, d and p are distinct real numbers such that (a² + b²+c²) p²-2p (ab+bc+cd) + (b²+c² + d²) ≤0, then a, b, c, d are in(a) AP(b) GP(c) HP(d) ab = cdvery short method by value put?.
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