Chapter A.7, Problem 63AYU

To determine

To find:The solution of given equation in complex number system.

Answer to Problem 63AYU

The solution of given equation in complex number systemis $\frac{1}{5}\pm \frac{2}{5}i$ .

Explanation of Solution

Given information:

The equationis $5x^2+1=2x$ .

Calculation:

Consider the equation.

  $\begin{array}{l}5x^2+1=2x\\ 5x^2-2x+1=0\\ x=\frac{-\left(-2\right)\pm \sqrt{{\left(-2\right)}^2-4\left(5\right)\left(1\right)}}{2\left(5\right)}\\ x=\frac{2\pm \sqrt{-16}}{10}\\ x=\frac{2\pm \sqrt{16}\sqrt{-1}}{10}\\ x=\frac{2\pm 4i}{10}\\ x=\frac{1}{5}\pm \frac{2}{5}i\end{array}$