(2x-1)2=(x+1)2 Brainly

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Jun 07, 2024

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Solve the Equation: (2x-1)² = (x+1)²

In this article, we will solve the equation (2x-1)² = (x+1)². This equation involves quadratic expressions on both sides, and we will use algebraic methods to find the solution.

Expanding the Equation

Let's start by expanding both sides of the equation using the formula (a+b)² = a² + 2ab + b².

(2x-1)² = (2x)² - 2(2x)(1) + 1² = 4x² - 4x + 1

(x+1)² = x² + 2(x)(1) + 1² = x² + 2x + 1

Now, we can equate the two expressions:

4x² - 4x + 1 = x² + 2x + 1

Simplifying the Equation

Let's simplify the equation by combining like terms:

4x² - 4x + 1 = x² + 2x + 1 3x² - 6x = 0

Factoring the Equation

We can factor out x from both terms:

x(3x - 6) = 0

This tells us that either x = 0 or 3x - 6 = 0.

Solving for x

Let's solve for x:

3x - 6 = 0 3x = 6 x = 2

So, the solutions to the equation are x = 0 and x = 2.

Conclusion

In this article, we solved the equation (2x-1)² = (x+1)² using algebraic methods. We expanded both sides of the equation, simplified it, and factored it to find the solutions x = 0 and x = 2.