Excel in math, science, and engineering

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\[ \large{\begin{array}{ccccccc} && & & & & A&A\\ && & & & & B&B\\ +&& & & & & C&C\\ \hline & & & & & A & B&C\\ \end{array}} \]

\[ \begin{array} { l l l } & A & B \\ & C & D \\ + & E & F \\ \hline & G & H \\ \end{array} \]

In the above cryptogram, all the ...

\[\large \frac{{(a}^{2}+1)({b}^{2}+1)}{(a-1)(b-1)} =\frac{ab+1}2\]

Given that real numbers \(a\) and \(b\), where \(a, b\ne 1\), satisfy the equation above ...

Let \(a\), \(b\) and \(c\) be non-negative real numbers such that \(a + b + c = 1\). Find the maximum value of \(10101(ab + bc + ca) - 12987abc.\)

\[\dfrac{a^2 + b^2 + c^2}{a+b+c} = d\]

Let \(a,b,c,d\) be distinct digits between \(1\) and \(9\) inclusively, satisfying the equation above. What is ...

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