Bunuel wrote:
\((x - 2)^2 + (x - 1)^2 + x^2 + (x + 1)^2 + (x + 2)^2 =\)
(A) \(5x^2\)
(B) \(5x^2 + 10\)
(C) \(x^2 + 10\)
(D) \(5x^2 + 6x + 10\)
(E) \(5x^2 - 6x + 10\)
Instead of jumping straight into the calculation, we'll first look at the answers.
This is an Alternative approach.
All of our answers are very similar - they are mostly quadratic equations of the form ax^2 + bx + c.
Let's look at each coefficient separately:
According to the answers a can be 1 or 5.
Looking at our equation, we see that we have 5 expressions, each of which gives one copy of x^2.
So a = 5.
(C) is eliminated.
b can be either 0, 6 or -6.
Looking at our expressions, we can see that our expression is symmetrical: (x - 2)^2 and (x+2)^2 cancel out as do (x - 1)^2 and (x + 1)^2.
So b must be 0. (D), (E) are eliminated.
Finally, c is 0 or 10. As it is the sum of positive numbers (2^2, 1^2, 1^2, 2^2), it can't be 0.
(A) is eliminated.
(B) is our answer.
Note that it is also perfectly possible to just straight up calculate the value of the expression.
Using the answers to guide your calculation can help avoid making silly mistakes.
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