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Algebra
Polynomial Inequalities
\[ \big(n^2-2\big)\big(n^2-20\big)<0\]
How many integers \(n\) satisfy the inequality above?
by
Piyush Maheshwari
Over the ranges
\[ \begin{eqnarray} -1 \leq & v & \leq 1 \\ -2 \leq & u & \leq -0.5 \\ -2 \leq & z & \leq -0.5 \\ \end{eqnarray} \]
what is the range of \(w = \frac {vz}{u} \)?
by
Sanjeet Raria
If \(x\) is an integer that satisfies the inequality
\[ 9 < x ^2 < 99, \]
find the difference between the maximum and minimum possible values of \(x.\)
by
Chung Kevin
As \(x\) and \(y\) ranges over all real values, what is the minimum value of
\[ (15x + 30y + 20)^2 + (20x + 40y + 15)^2? \]
by
Calvin Lin
Given \(y=\frac{2x}{1+x^{2}}\), where \(x\) and \(y\) are real numbers, what is the range of \(y^{2}+y-2\)?
by
Sandeep Bhardwaj