Follow up to Angie's question?
If both sides are not = then why is there an equal sign? And is the answer 2 or both 2 and -1? Thanks!
The quadratic equation yields two solutions:
x = 2 and x = -1
But that quadratic equation is not equivalent to the original equation. What you know for sure is that any solution of the original equation will also satisfy the quadratic equation. That means that the quadratic equation can have more solutions that the original equation has.
You can check that x = 2 is a solution and that x = -1 is not a solution.
A deeper reason why you got the extra solution is that the square root function is defined to be the positive inverse of the function y = x^2. This function has two inverses that are negatives of each other.
When you obtained the quadratic equation by squaring both sides, you only used the fact that the square root is an inverse of the quadratic function, not that it is the positve inverse. This means that had we defined the square root functon as the negative inverse, we would have obtained the same quadratic equation. The solution of the quadratic equation will thus also contain the solution of the equation with the square root replaced by its negative.
Let's check this:
-sqrt(3-x) for x = -1 is equal to -2
x - 1 for x = -1 is equal to -2.
Thank you Count Iblis for the great explanation and confirmation of my objection to that post.
This is in reference to
http://www.jiskha.com/display.cgi?id=1247010204
To answer your question, allow me to clarify a few things about the equal sign and the process of solving equations.
The equal sign (=) in an equation is used to establish a balance between two expressions. It indicates that the value on the left side is equal to the value on the right side. In other words, both sides of the equation represent the same quantity.
When you solve an equation, the goal is to find the value(s) of the unknown variable that satisfy the equation. Depending on the equation, there can be one solution, infinitely many solutions, or no solution.
Now let's address Angie's question directly. If both sides of an equation are not equal (as Angie mentioned), it means that the equation is not balanced or does not hold true. In such cases, the equation does not have a solution, and we say it is an inconsistent equation.
Regarding the specific values you mentioned (2 and -1), without the equation or further context, it is challenging for me to determine whether these values are correct solutions. However, keep in mind that an equation can have one or multiple solutions, or sometimes, no solutions at all.
To determine the solutions of an equation, you need to analyze the given equation and apply appropriate mathematical operations to isolate the variable on one side of the equation. This process leads to finding the specific value(s) that make the equation true.
If you can provide the equation or further details, I would be happy to assist you in solving it and verifying the solutions!