Question

What are the solutions of x^2-3x+3=0

Answer 1

The solutions to quadratic equation are:

$x = \frac{3 + i \sqrt{3}}{2}\\\\x = \frac{3 - i \sqrt{3}}{2}$

Solution:

Given is:

$x^2 - 3x + 3 = 0$

We have to find the solutions to quadratic equation

$\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\\\x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\mathrm{For\:}\quad a=1,\:b=-3,\:c=3:\\\\x=\frac{-\left(-3\right)\pm \sqrt{\left(-3\right)^2-4\cdot \:1\cdot \:3}}{2\cdot \:1}$

$x=\frac{3 \pm \sqrt{\left(-3\right)^2-4\cdot \:1\cdot \:3}}{2\cdot \:1}\\\\x = \frac{3 \pm \sqrt{-3}}{2}\\\\x = \frac{3 \pm i \sqrt{3}}{2}$

We have two solutions :

$x = \frac{3 + i \sqrt{3}}{2}\\\\x = \frac{3 - i \sqrt{3}}{2}$