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If A B and C are real numbers and A²+B²+C²=1 then AB+BC+CA=1 then AB+BC+CA can take values:-?
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If A B and C are real numbers and A²+B²+C²=1 then AB+BC+CA=1 then AB+B...
1. Given Information:
Given that A, B, and C are real numbers such that A² + B² + C² = 1.
2. Relationship between A, B, C:
We are also given that AB + BC + CA = 1.
To understand the relationship between A, B, and C in terms of AB + BC + CA, let's consider the expansion of (A + B + C)².
3. Expansion of (A + B + C)²:
(A + B + C)² = A² + B² + C² + 2AB + 2BC + 2CA
= 1 + 2(AB + BC + CA)
4. Using the given information:
From the given information, we know that A² + B² + C² = 1.
Substitute this into the expansion of (A + B + C)²:
(A + B + C)² = 1 + 2(AB + BC + CA)
5. Substitute back into the equation:
Since (A + B + C)² = 1 + 2(AB + BC + CA), we have:
1 = 1 + 2(AB + BC + CA)
6. Solving for AB + BC + CA:
Rearranging the equation, we get:
AB + BC + CA = 0
7. Conclusion:
Therefore, AB + BC + CA can take the value of 0 when A² + B² + C² = 1. This relationship holds true for any real numbers A, B, and C that satisfy the given condition.
Given that A, B, and C are real numbers such that A² + B² + C² = 1.
2. Relationship between A, B, C:
We are also given that AB + BC + CA = 1.
To understand the relationship between A, B, and C in terms of AB + BC + CA, let's consider the expansion of (A + B + C)².
3. Expansion of (A + B + C)²:
(A + B + C)² = A² + B² + C² + 2AB + 2BC + 2CA
= 1 + 2(AB + BC + CA)
4. Using the given information:
From the given information, we know that A² + B² + C² = 1.
Substitute this into the expansion of (A + B + C)²:
(A + B + C)² = 1 + 2(AB + BC + CA)
5. Substitute back into the equation:
Since (A + B + C)² = 1 + 2(AB + BC + CA), we have:
1 = 1 + 2(AB + BC + CA)
6. Solving for AB + BC + CA:
Rearranging the equation, we get:
AB + BC + CA = 0
7. Conclusion:
Therefore, AB + BC + CA can take the value of 0 when A² + B² + C² = 1. This relationship holds true for any real numbers A, B, and C that satisfy the given condition.
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If A B and C are real numbers and A²+B²+C²=1 then AB+BC+CA=1 then AB+BC+CA can take values:-?
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If A B and C are real numbers and A²+B²+C²=1 then AB+BC+CA=1 then AB+BC+CA can take values:-? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If A B and C are real numbers and A²+B²+C²=1 then AB+BC+CA=1 then AB+BC+CA can take values:-? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If A B and C are real numbers and A²+B²+C²=1 then AB+BC+CA=1 then AB+BC+CA can take values:-?.
If A B and C are real numbers and A²+B²+C²=1 then AB+BC+CA=1 then AB+BC+CA can take values:-? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If A B and C are real numbers and A²+B²+C²=1 then AB+BC+CA=1 then AB+BC+CA can take values:-? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If A B and C are real numbers and A²+B²+C²=1 then AB+BC+CA=1 then AB+BC+CA can take values:-?.
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