1957 AHSME Problems/Problem 14

If $y = \sqrt{x^2 - 2x + 1} + \sqrt{x^2 + 2x + 1}$ , then $y$ is:

$\textbf{(A)}\ 2x\qquad \textbf{(B)}\ 2(x+1)\qquad\textbf{(C)}\ 0\qquad\textbf{(D)}\ |x-1|+|x+1|\qquad\textbf{(E)}\ \text{none of these}$

Solution

In order to solve the problem, we will use two properties, namely, that $(a+b)^2=a^2+2ab+b^2$ and $(a-b)^2=a^2-2ab+b^2$ .

We can use this to simplify the equation, as $y = \sqrt{x^2 - 2x + 1} + \sqrt{x^2 + 2x + 1}$ turns into $y = x + 1 + x - 1$ . $y$ is $\boxed{\textbf{(A) }2x}$ .

1957 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 13	Followed by Problem 15
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1957 AHSME Problems/Problem 14

Solution

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