If e = (x – 5)^2 + (x + 1)^2 – 6, then y is least when x =  Select the correct option
A) -2 B) -1 C) 0 D) 2 E) None of the above
Let us transform the formula:   e = (x – 5)² + (x +1)² – 6 =   x² – 10x + 25 + x² + 2x + 1 – 6 =   2x² – 8x + 20 = 2 × (x² – 4x + 10) =   2 × ((x² – 4x + 4) + 6) =   2 × ((x – 2)² + 6)   Any square is greater or equal 0. Therefore the formula possess the least value when (x – 2)² = 0.   x – 2 = 0   x = 2   The correct answer is choice (2).
<result>D</result>
If e = (x – 5)^2 + (x + 1)^2 – 6, then y is least when x =