Inequalities

Let $$ x, y $$, and $$ z $$ be real numbers satisfying: $$ 4(x^2 + y^2 + z^2) = a $$ $$ 4(x - y - z) = 3 + a $$ Th...

For natural numbers $$x$$, $$y$$, and $$z$$, if $$xy + yz = 19$$ and $$yz + xz = 51$$, then the minimum possible value ...

![Screenshot 2025-04-02 181838.png](https://res.cloudinary.com/aptidude/image/upload/v1743598881/aptidude_questions/njzp...

All the values of $$x$$ satisfying the inequality $$\frac{1}{x+5} \leq \frac{1}{2x-3}$$ are: ...