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Let \(x, y, z\) be real numbers such that \(x^{2}+y^{2}+z^{2}=1\). Find the maximum possible value of \(\sqrt {10} xy+yz\).

Find the number of real solutions of the equation \[ \frac{1}{[x]}+\frac{1}{[2x]}= x-[x]+\frac{1}{3}. \]

Note: 1.\([x]\) stands for the greatest integer function. 2 ...

\(x,y\) are reals satisfying \[x^2+y^2=\left(\dfrac{x}{y}+\dfrac{y}{x}\right)^2\] The double-sided inequality ...

If the range of positive \(x\) satisfy the equation \( \lceil x \lfloor x \rfloor \rceil + \lfloor x \lceil x \rceil \rfloor = 111 \) is \( \alpha \leq x \leq \beta \). What is ...

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