Equations Involving One Variable Leading to Quadratic Equation| Algebra| ENGG10 LE3| Problem 4

If a regular polygon of ten sides is inscribed in a circle of radius r units, then, if s units is the length of the side, r/s=s/(r-s) Solve this formula for s in terms of r.

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Differential and Integral Calculus by Feliciano and Uy, Exercise 1.1, Problem 2

If $latex y=\frac{x^2+3}{x}&s=3&fg=000000$, find x as a function of y. SOLUTION: $latex y=\frac{x^2+3}{x}&s=1&fg=000000$ $latex xy=x^2+3&s=1&fg=000000$ $latex x^2-xy+3=0&s=1&fg=000000$ Solve for x using quadratic formula. We have $latex a=1,\:b=-y,\:and\:c=3&s=1&fg=000000$ $latex x=\frac{-b\pm \sqrt{b^2-4ac}\:}{2a}&s=1&fg=000000$ $latex x=\frac{\cdot -\left(-y\right)\pm \sqrt{\left(-y\right)^2-4\left(1\right)\left(3\right)}}{2\left(1\right)}&s=1&fg=000000$ $latex x=\frac{y\pm \sqrt{y^2-12}}{2}&s=1&fg=000000$