Question

Find the solutions of
`y=x^(2)+2` and
`y=x+1`

Answer 1

x is
`(1\ + √(3) i)/(2)` AND

`(1\ - √(3) i)/(2)`

y =
`(3\ + √(3) i)/(2)` And

`(3\ - √(3) i)/(2)`

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* a* c}}{2* a}`

Or, x =
`\frac{1\pm \sqrt{-1^(2)-4* 1* 1}}{2* 1}`

Or , x =
`(1\pm √(-3))/(2)`

Hence the two value of x is
`(1\ + √(3) i)/(2)` AND

`(1\ - √(3) i)/(2)`

So , y =
`(3\ + √(3) i)/(2)` And

`(3\ - √(3) i)/(2)`