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\[\large \begin{cases} ab+c+d=15 \\ bc+a+d=19 \\ cd+a+b=25 \\ ad+b+c=17 \end{cases} \]

Positives integers \(a\), \(b\), \(c\) and \(d\) satisfy the ...

Two ladders--9 meters and 6 meters high each--are set up in an alley such that one ladder leans from the base of the left wall to the right wall, and ...

\[\large \begin{cases} \dfrac{x+y}{x-y} + \dfrac{x-y}{x+y} = \dfrac 52 \\ x^2+y^2 = 90 \\ \end{cases}\]

Find the minimum value of \(y-x\)

What is the next term in this infinite sum?

\[\large 1- \frac{1}{2}x^2 + \frac{1}{24}x^4 - \frac{1}{720}x^6 + . . .\]

Hint: The terms simply ...

\[\large \lim_{x\to\infty} x^2\ln(x\cot^{-1}x)=?\]

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