Question

If A=x+y,B= a - y,c=x+2y, then a^2+b^2+c^2 - ab- bc - ca = Ky^2

Find K:-???
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Answer 1

If a = x+y, b = x - y, c = x+2y, then a^2 + b^2 + c^2 - ab- bc - ca = Ky^2

Find K:-??? (correct question)

Given:

a = x+y , b = x - y, c = x+2y

a^2+b^2+c^2 - ab- bc - ca = Ky^2

To Find:

Find the value of the K.

Solution:

1) By the formula we all know that

  a² + b² + c² - ab- bc - ca = 1/2 [(a-b)² + (b-c)² + (a-c)²]

2) Now put the value of the a, b, and c in the equation given above:

  LHS

•    1/2 [(a-b)² + (b-c)² + (a-c)²]

•   1/2 [ ( x+y - x+y)² + (x-y - x-2y)² + (x+y - x-2y)²]

•   1/2 [(2y)² + (-3y)² + (-y)²]

•   1/2[4y² + 9y² + y²]

•   1/2[14y²]

•   7y²

3) Now equate the term with RHS

we get

   7y² = ky²

By comparing the equation we get the value of K is 7