*v*

2

 − 

2

 = 

1



*v* = 

Submit


To solve the equation:

\[
v^2 - 2 = 1
\]

We follow these steps:

### Step 1: Add 2 to both sides
\[
v^2 - 2 + 2 = 1 + 2
\]
\[
v^2 = 3
\]

### Step 2: Take the square root of both sides
\[
v = \pm \sqrt{3}
\]

Thus, the solution is:
\[
v = \pm \sqrt{3}
\]

Would you like further details or have any questions?

### Related Questions:
1. How do you simplify square roots?
2. What are the properties of quadratic equations?
3. Can a quadratic equation have more than two solutions?
4. What is the significance of the ± symbol in the solution?
5. How do we solve equations with higher powers like \(v^3\)?

**Tip:** Always check your solutions by substituting them back into the original equation.

Understand how to solve the quadratic equation v^2 - 2 = 1 with a detailed step-by-step solution. This problem covers key algebraic concepts like solving quadratic equations and using square roots, ideal for students in Grades 7-9.

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