Respuesta :
Answer:
x is [tex]\frac{1\ + \sqrt{3} i}{2}[/tex] AND
[tex]\frac{1\ - \sqrt{3} i}{2}[/tex]
y = [tex]\frac{3\ + \sqrt{3} i}{2}[/tex] And
[tex]\frac{3\ - \sqrt{3} i}{2}[/tex]
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 = [tex]\frac{-b\pm \sqrt{b^{2}-4\times a\times c}}{2\times a}[/tex]
Or, x = [tex]\frac{1\pm \sqrt{-1^{2}-4\times 1\times 1}}{2\times 1}[/tex]
Or , x = [tex]\frac{1\pm \sqrt{-3}}{2}[/tex]
Hence the two value of x is [tex]\frac{1\ + \sqrt{3} i}{2}[/tex] AND
[tex]\frac{1\ - \sqrt{3} i}{2}[/tex]
So , y = [tex]\frac{3\ + \sqrt{3} i}{2}[/tex] And
[tex]\frac{3\ - \sqrt{3} i}{2}[/tex]
