Excel in math, science, and engineering

1.(a). If \(a,b,c\) are positive reals and \(a+b+c=50\) and \(3a+b-c=70\). If \(x=5a+4b+2c\), find the range of the values of ...

Given that \(a,b,c>0 \), prove that

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Hello everyone!, I am happy to announce the Math Olympiad Contest which only allows High School Math problems. I am organizing this contest so as to get exposure to various ...

\[\dfrac {a^k}{(a-b)(a-c)} + \dfrac {b^k}{(b-a)(b-c)} + \dfrac {c^k}{(c-a)(c-b)} > \dfrac {k(k-1)}{2}\]

If \(a\), \(b\) and \(c\) are distinct positive reals such ...

By the fundamental theorem of arithmetic, every positive integer greater than 1 can be written as a product of primes. Thus, we can write every positive integer as ...

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