Difference between revisions of "2020 IMO Problems/Problem 2"
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On that case we get ,<cmath>(a+2b+3c+4d) a^ab^bc^c \le (a+2b+3c+4d)(a^2+b^2+c^2+d^2) =\frac{5}{8} <1</cmath> | On that case we get ,<cmath>(a+2b+3c+4d) a^ab^bc^c \le (a+2b+3c+4d)(a^2+b^2+c^2+d^2) =\frac{5}{8} <1</cmath> | ||
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Revision as of 23:34, 26 September 2020
Problem 2. The real numbers are such that and . Prove that
Solution
Using Weighted AM -GM we get,
So,
Now notice that ,
So, We get ,
Now , For equality we must have
On that case we get ,
~ftheftics