If a² + b² + c² = 2(a + c - 1), then find the value of a³ + b³ + c³.

If the mean of $$ p, q, r $$ is $$ M $$ and $$ pq + qr + rp = 0 $$, then the mean of $$ p^2, q^2, r...

If $$ x $$ is an odd integer, which of the following statements is correct? ...

If $$\sqrt{5x + 9} + \sqrt{5x - 9} = 3(2 + \sqrt{2}),$$ then $$\sqrt{10x + 9} \text{ is equal to ...

The number of integer solutions of the equation $$ 2|x|(x^2 + 1) = 5x^2 $$ is: ...

If $$p^2 + q^2 - 29 = 2pq - 20 = 52 - 2pq$$, then the difference between the maximum and minimum po...

If $$x$$ and $$y$$ vary inversely to each other, and $$x = 7$$ when $$y = 12$$, find $$y$$ when $$x ...