Difference between revisions of "1968 AHSME Problems/Problem 28"
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setting <math>x=\sqrt{\frac{a}{b}}</math> we get a quadratic equation is<math>x^2+1=4x</math> with solutions <math>x=\frac{4\pm \sqrt{16-4}}{2}</math> | setting <math>x=\sqrt{\frac{a}{b}}</math> we get a quadratic equation is<math>x^2+1=4x</math> with solutions <math>x=\frac{4\pm \sqrt{16-4}}{2}</math> | ||
− | <math>x^2=\frac{a}{b}=(4+3)+4\sqrt{3} | + | <math>x^2=\frac{a}{b}=(4+3)+4\sqrt{3}=13.8=14</math>. |
== See also == | == See also == |
Latest revision as of 06:31, 27 January 2019
Problem
If the arithmetic mean of and is double their geometric mean, with , then a possible value for the ratio , to the nearest integer, is:
Solution
setting we get a quadratic equation is with solutions
.
See also
1968 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 27 |
Followed by Problem 29 | |
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 |
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