Difference between revisions of "2015 Final tour - Azerbaijan in lower age category"
(Created page with "1) a, b, and c are positive real numbers that abc=1/8. Prove a^2+b^2+c^2+a^2*b^2+a^2*c^2+b^2*c^2>=15/16") |
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1) a, b, and c are positive real numbers that abc=1/8. Prove | 1) a, b, and c are positive real numbers that abc=1/8. Prove | ||
| − | a^2+b^2+c^2+a^2*b^2+a^2*c^2+b^2*c^2>=15/16 | + | a^2+b^2+c^2+a^2*b^2+a^2*c^2+b^2*c^2>=15/16 (2 points) |
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| + | 2) a, b and c are sides of triangle. Prove that area of triangle isn't more than (a^2+b^2+c^2)/6. | ||
Revision as of 02:23, 27 June 2015
1) a, b, and c are positive real numbers that abc=1/8. Prove a^2+b^2+c^2+a^2*b^2+a^2*c^2+b^2*c^2>=15/16 (2 points)
2) a, b and c are sides of triangle. Prove that area of triangle isn't more than (a^2+b^2+c^2)/6.
