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∫

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1

Solved example of radical equations and functions

$Y^2-Y^1+Y+1=0$

2

Any expression to the power of $1$ is equal to that same expression

$y^2-y+y+1=0$

3

Subtracting $y$ and $y$

$1+y^2=0$

4

Subtract $1$ from both sides of the equation

$y^2=0-1$

5

$x+0=x$, where $x$ is any expression

$y^2=-1$

6

Removing the variable's exponent

$y=\pm \sqrt{-1}$

7

Calculate the power using complex numbers

$y=\pm 1i$

8

Any expression multiplied by $1$ is equal to itself

$y=\pm i$

9

As in the equation we have the sign $\pm$, this produces two identical equations that differ in the sign of the term $i$. We write and solve both equations, one taking the positive sign, and the other taking the negative sign

$y=i,\:y=-i$

10

Solve the equation ($1$)

$y=i$

11

Solve the equation ($2$)

$y=-i$

12

The $2$ solutions of the equation are

$y=i,\:y=-i$