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a2 + b2 + c2 – ab – bc – ca equals:
- a)
- b)
- c)
- d)
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
a2+ b2+ c2– ab – bc – ca equals:a)b)c)d)Correct answ...
= ( a² + b² + c² - ab - bc - ca )
By multiplying it by 2 and dividing it by 2.
= 2 ( a² + b² + c² - ab - bc - ca ) ÷ 2
= ( 2a² + 2b² + 2c² - 2ab - 2bc - 2ca ) ÷ 2
= ( a² + a² + b² + b² + c² + c² - 2ab - 2bc - 2ca ) ÷ 2
= ( a² + b² - 2ab + b² + c² - 2bc + a² + c² - 2ca ) ÷ 2
= [ ( a - b )² + ( b - c )² + ( a - c )² ] ÷ 2
Now , whatever is the value of ( a - b ) , ( b - c ) and ( a - c ) but its square will be always positive, and 2 is also a positive number.
So, the sum of ( a - b )², ( b - c )² and ( a - c )² will be a positive number and if a positive number is divided by a positive number then the result is also a positive number.
So, it is a positive number,hence it can't be a negative number.
Most Upvoted Answer
a2+ b2+ c2– ab – bc – ca equals:a)b)c)d)Correct answ...
= ( a² + b² + c² - ab - bc - ca )
By multiplying it by 2 and dividing it by 2.
= 2 ( a² + b² + c² - ab - bc - ca ) ÷ 2
= ( 2a² + 2b² + 2c² - 2ab - 2bc - 2ca ) ÷ 2
= ( a² + a² + b² + b² + c² + c² - 2ab - 2bc - 2ca ) ÷ 2
= ( a² + b² - 2ab + b² + c² - 2bc + a² + c² - 2ca ) ÷ 2
= [ ( a - b )² + ( b - c )² + ( a - c )² ] ÷ 2
Now , whatever is the value of ( a - b ) , ( b - c ) and ( a - c ) but its square will be always positive, and 2 is also a positive number.
So, the sum of ( a - b )², ( b - c )² and ( a - c )² will be a positive number and if a positive number is divided by a positive number then the result is also a positive number.
So, it is a positive number,hence it can't be a negative number.
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a2+ b2+ c2– ab – bc – ca equals:a)b)c)d)Correct answ...
=1/2 [(a-b)² + (b-c)² + +(c-a)²] =1/2 ( a² -2ab+b² +b² -2bc +c² +c² - 2ca + a²)= 1/2 ( a²+a² + b² +b² + c² + c² -2ab -2bc-2ca)= 1/2 (2a² +2b²+ 2 c² -2ab -2bc-2ca) =2× 1/2 ( a²+ b²+c²-ab. -bc -ca) by taking 2 as common =1 (a²+b²+c²-ab-bc-ca)= a²+b² +c² -ab- bc-ca
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a2+ b2+ c2– ab – bc – ca equals:a)b)c)d)Correct answer is option 'D'. Can you explain this answer?
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a2+ b2+ c2– ab – bc – ca equals:a)b)c)d)Correct answer is option 'D'. Can you explain this answer? for Class 8 2025 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about a2+ b2+ c2– ab – bc – ca equals:a)b)c)d)Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 8 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for a2+ b2+ c2– ab – bc – ca equals:a)b)c)d)Correct answer is option 'D'. Can you explain this answer?.
a2+ b2+ c2– ab – bc – ca equals:a)b)c)d)Correct answer is option 'D'. Can you explain this answer? for Class 8 2025 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about a2+ b2+ c2– ab – bc – ca equals:a)b)c)d)Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 8 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for a2+ b2+ c2– ab – bc – ca equals:a)b)c)d)Correct answer is option 'D'. Can you explain this answer?.
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