Difference between revisions of "1958 AHSME Problems/Problem 5"
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==Solution== | ==Solution== | ||
| − | + | We have | |
| − | {{ | + | <cmath>\begin{align*}2+\sqrt{2}+\frac{2-\sqrt{2}}{4-2}+\frac{\sqrt{2}+2}{2-4}&=2+\sqrt{2}+\frac{1}{2}(2-\sqrt{2})-\frac{1}{2}(\sqrt{2}+2)\\&=\frac{1}{2}(2+\sqrt{2}+2-\sqrt{2})\\&= \boxed{\text{(A) }2}.</cmath> |
==See also== | ==See also== | ||
{{AHSME box|year=1958|num-b=4|num-a=6}} | {{AHSME box|year=1958|num-b=4|num-a=6}} | ||
Revision as of 13:19, 4 June 2011
Problem
The expression 
equals:
Solution
We have
\begin{align*}2+\sqrt{2}+\frac{2-\sqrt{2}}{4-2}+\frac{\sqrt{2}+2}{2-4}&=2+\sqrt{2}+\frac{1}{2}(2-\sqrt{2})-\frac{1}{2}(\sqrt{2}+2)\\&=\frac{1}{2}(2+\sqrt{2}+2-\sqrt{2})\\&= \boxed{\text{(A) }2}. (Error compiling LaTeX. Unknown error_msg)
See also
| 1958 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 4 |
Followed by Problem 6 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
| All AHSME Problems and Solutions | ||
