Sir , how to solve the question in the attachment ?

Ans: x=+3 or x=-3

To solve the equation that leads to the solutions \( x = +3 \) or \( x = -3 \), we first need to understand the context of the problem. It sounds like you might be dealing with a quadratic equation or a situation involving absolute values. Let’s break down how we arrive at those solutions step by step.

Understanding the Equation

Assuming the equation you are working with is something like \( x^2 = 9 \) or \( |x| = 3 \), both of these yield the solutions \( x = +3 \) and \( x = -3 \). Let’s look at each case.

Case 1: Quadratic Equation

If we have the equation:

• x² = 9

To solve for \( x \), we take the square root of both sides. Remember that when you take the square root, you must consider both the positive and negative roots:

• √(x²) = ±√9
• Thus, x = ±3

Case 2: Absolute Value Equation

For an absolute value equation like:

• |x| = 3

The absolute value of a number is its distance from zero on the number line, which means it can be either positive or negative. Therefore, we can set up two separate equations:

• x = 3
• x = -3

Verifying the Solutions

It’s always a good practice to verify our solutions by substituting them back into the original equation. For both cases:

• For \( x = 3 \):
• In \( x^2 = 9 \): \( 3^2 = 9 \) (True)
• In \( |x| = 3 \): \( |3| = 3 \) (True)
• For \( x = -3 \):
• In \( x^2 = 9 \): \( (-3)^2 = 9 \) (True)
• In \( |x| = 3 \): \( |-3| = 3 \) (True)

Conclusion

Both methods confirm that the solutions \( x = +3 \) and \( x = -3 \) are indeed correct. If your equation differs from these examples, feel free to share it, and I can help you work through it specifically. Understanding the principles behind solving equations will make it easier to tackle similar problems in the future!