Question

Julie says that she can perform a magic trick with numbers. She asks you to pick a whole number, any whole number. Square that number. Then add twice the your original number. Next add 1. Take the square root of the result. Finally, subtract your original number. Then Julie exclaims with authority, "Your answer is 1." Is your answer 1?

Answer 1

By algebraically following the steps provided with any whole number represented as 'x', the final result is proven to be 1, supporting Julie's claim.

Step-by-step explanation:

The student's question involves a sequence of mathematical operations on a chosen whole number. To verify Julie's claim that the final result is always 1, we need to follow the steps algebraically. Let's take a variable 'x' as our original number.

1. Square 'x': x².
2. Add twice the original number: x² + 2x.
3. Add 1: x² + 2x + 1.
4. Take the square root: √(x² + 2x + 1) which simplifies to x + 1 because the expression is a perfect square (x+1)².
5. Subtract the original number: (x + 1) - x, which equals 1.

Therefore, no matter the original whole number chosen, following Julie's steps will indeed always result in the number 1.