Multiply a² + b² + c² - ab - bc - ca by a + b + c.
Answers
Answer:
Correction : a² + b² + c² - ab - bc - ca.
= ( 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.
Proved.
Hope it helps !
Mark me as Brainliest
Xmarty AdiTi
