1974 AHSME Problems/Problem 20
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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 | |
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