Difference between revisions of "1954 AHSME Problems/Problem 14"
Katzrockso (talk | contribs) (Created page with "== Problem 14== When simplified <math>\sqrt{1+ \left (\frac{x^4-1}{2x^2} \right )^2}</math> equals: <math>\textbf{(A)}\ \frac{x^4+2x^2-1}{2x^2} \qquad \textbf{(B)}\ \frac{x...") |
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== Solution == | == Solution == | ||
| − | <math>\sqrt{\frac{4x^4}{4x^4}+\frac{(x^4-1)^2}{4x^4}}\implies\sqrt{\frac{x^8-2x^4+1+4x^4}{4x^4}}\implies \sqrt{\frac{(x^4+1)^2}{2x^2}}\implies \frac{x^4+1}{2x^2}\implies\frac{x^2}{2}+\frac{1}{2x^2}</math>, <math>\fbox{E}</math> | + | <math>\sqrt{\frac{4x^4}{4x^4}+\frac{(x^4-1)^2}{4x^4}}\implies\sqrt{\frac{x^8-2x^4+1+4x^4}{4x^4}}\implies \sqrt{\frac{(x^4+1)^2}{(2x^2)^2}}\implies \frac{x^4+1}{2x^2}\implies\frac{x^2}{2}+\frac{1}{2x^2}</math>, <math>\fbox{E}</math> |
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| + | ==See Also== | ||
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| + | {{AHSME 50p box|year=1954|num-b=13|num-a=15}} | ||
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| + | {{MAA Notice}} | ||
Latest revision as of 01:26, 28 February 2020
Problem 14
When simplified 
equals:
Solution
, 
See Also
| 1954 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 13 |
Followed by Problem 15 | |
| 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 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
