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Given \[a-b=\sqrt{42+12\sqrt{6}}, b-c=\sqrt{42-12\sqrt{6}},\] what is the value of \[a^2+b^2+c^2-ab-bc-ca?\]

\(a\), \(b\) and \(c\) are real numbers such that \[a+b+c \neq 0, a^3+b^3+c^3=36, abc=12.\] What is the value of ...

Let \(m\) and \(n\) be the two roots of the equation \(x^2+ax+b=0,\) where \(a\) and \(b\) are constants. If the two roots of ...

\(a\) is a positive integer and the cubic polynomial \[x^3-15x^2+(14+a)x-a\] can be factorized as the product of \(3\) distinct linear polynomials with real coefficients. What ...

Evaluate \[\frac{(177 ^2-175 ^2)(173 ^2-171 ^2)(169 ^2-167 ^2)}{176 \times 172 \times 168}.\]

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