Difference between revisions of "1974 AHSME Problems/Problem 20"
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{{AHSME box|year=1974|num-b=19|num-a=21}} | {{AHSME box|year=1974|num-b=19|num-a=21}} | ||
+ | [[Category:Introductory Algebra Problems]] | ||
+ | {{MAA Notice}} |
Latest revision as of 11:43, 5 July 2013
Problem
Let
\[T=\frac{1}{3-\sqrt{8}}-\frac{1}{\sqrt{8}-\sqrt{7}}+\frac{1}{\sqrt{7}-\sqrt{6}}-\frac{1}{\sqrt{6}-\sqrt{5}}+\frac{1}{\sqrt{5}-2}.\] (Error making remote request. Unexpected URL sent back)
Then
Solution
Let's try to rationalize . Multiplying the numerator and denominator by gives us .
Therefore,
Hence the answer is .
See Also
1974 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 19 |
Followed by Problem 21 | |
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.