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...") |
Katzrockso (talk | contribs) (→Solution) |
||
Line 6: | Line 6: | ||
== 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> |
Revision as of 12:14, 6 June 2016
Problem 14
When simplified equals:
Solution
,