Question

Find the solutions of align="absmiddle" class="latex-formula"> and $y=x+1$

Answer 1

Answer:

x is  $\frac{1\ + \sqrt{3} i}{2}$   AND

       $\frac{1\ - \sqrt{3} i}{2}$

y = $\frac{3\ + \sqrt{3} i}{2}$      And

      $\frac{3\ - \sqrt{3} i}{2}$

Step-by-step explanation:

Given two equations are :

y = x² + 2         And

y = x + 1

So, the equation can be written as

x² + 2  =  x + 1

Or, x² - x + ( 2 - 1) = 0

Or, x² - x + 1 = 0

This is in the form of quadratic equation

So,   Roots of equation x be :

     x = $\frac{-b\pm \sqrt{b^{2}-4\times a\times c}}{2\times a}$

Or, x = $\frac{1\pm \sqrt{-1^{2}-4\times 1\times 1}}{2\times 1}$

Or , x = $\frac{1\pm \sqrt{-3}}{2}$

Hence the two value of x is  $\frac{1\ + \sqrt{3} i}{2}$   AND

                                               $\frac{1\ - \sqrt{3} i}{2}$

So , y = $\frac{3\ + \sqrt{3} i}{2}$      And

              $\frac{3\ - \sqrt{3} i}{2}$