Sign up to access problem solutions.

Already have an account? Log in here.

Gauss, Ramanujan, and a pantheon of other mathematicians have given us algebraic manipulation tools way beyond what's taught in school. Learn what they knew.

Sign up to access problem solutions.

Already have an account? Log in here.

\[ \large x^{63} + x^{44} + x^{37} + x^{31} + x^{26} + x^9 + 6 \]

If \(x\) satisfies the equation \( \left(x + \dfrac1x\right)^2 = 3 \), then find the value of the expression above.

Sign up to access problem solutions.

Already have an account? Log in here.

Given that \(a^2 + b^2 = c^2 + d^2 = 85\) and \(|ac - bd| = 40,\) find \(|ad + bc|\).

Sign up to access problem solutions.

Already have an account? Log in here.

\[\large S = 2014^{3}-2013^{3}+2012^{3}-2011^{3}+\cdots+2^{3}-1^{3}\]

What is the largest perfect square that divides \(S\) above?

Sign up to access problem solutions.

Already have an account? Log in here.

\[\large 2016^{x}+2016^{-x}=3\]

\[\large \sqrt{\frac{2016^{6x}-2016^{-6x}}{2016^{x}-2016^{-x}}} = \, ?\]

Sign up to access problem solutions.

Already have an account? Log in here.

×

Problem Loading...

Note Loading...

Set Loading...