<p>There are exactly three positive real numbers <img alt="$k$" height="12" src="https://latex.artofproblemsolving.com/8/c/3/8c325612684d41304b9751c175df7bcc0f61f64f.png" width="9" /> such that the function<img alt="\[f(x)=\frac{(x-18)(x-72)(x-98)(x-k)}{x}.\]" height="38" src="https://latex.artofproblemsolving.com/0/d/b/0dbe0a5b2a8136e0b1e02478bc822fe2ba6ada41.png" width="318" />defined over the positive real numbers achieves its minimum value at exactly two positive real numbers <img alt="$x$" height="10" src="https://latex.artofproblemsolving.com/2/6/e/26eeb5258ca5099acf8fe96b2a1049c48c89a5e6.png" width="12" />. Find the sum of these three values of</p>

Question No: 332

There are exactly three positive real numbers $k$ such that the function $f(x)=\frac{(x-18)(x-72)(x-98)(x-k)}{x}.$ defined over the positive real numbers achieves its minimum value at exactly two positive real numbers $x$ . Find the sum of these three values of

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Tags: Algebra

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