How to Solve the Equation y^2+z^2=1 - Comprehensive Guide

Are you trying to find the exact solutions to the equation y^2+z^2=1? Solving this type of equation can be tricky but it is very doable. In this guide, we will walk through step-by-step the process of solving this equation.

Isolate the Variable

The first step to solving the equation is to isolate the variable we want to solve for. In this case, we want to solve for z so move it all to one side.

We start by subtracting y^2 from both sides of the equation, isolating z^2:

y^2+z^2 = 1
-y^2      -y^2

z^2 = 1 - y^2

Taking the Square Root of Both Sides

Now, we will take the square root of both sides of our equation, giving us two solutions.

√(z^2) = √(1-y^2)

We can now rewrite our equation as:

z = ±√(1-y^2)

Find the Solutions

This gives us two solutions, one positive and one negative.

z = √(1-y^2)

z = -√(1-y^2)


What are the solutions of the equation y^2+z^2=1?

The solutions of the equation y^2+z^2=1 are z = √(1-y^2) and z = -√(1-y^2).

Does solving the equation y^2+z^2=1 require any special techniques?

Yes, in order to solve the equation y^2+z^2=1, you will need to use the technique of isolating the variable as well as taking the square root of both sides of the equation.

What should I do if I'm having trouble solving the equation y^2+z^2=1?

If you're having trouble solving the equation y^2+z^2=1, make sure to carefully go through each step and understand the technique required to solve the equation. You may also want to get help from a tutor if needed.

What type of equation is y^2+z^2=1?

The equation y^2+z^2=1 is a quadratic equation.

How do I know when I have solved the equation y^2+z^2=1 correctly?

You will know you have solved the equation y^2+z^2=1 correctly when your answer is in the form of z = ±√(1-y^^2).

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