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Do Radical equations sometimes have extraneous solutions?
Yes, radical equations can sometimes have extraneous solutions. When solving these equations, squaring both sides to eliminate the radical can introduce solutions that do not satisfy the original equation. Therefore, it is essential to check all potential solutions in the original equation to verify their validity.
CAn someone help me with my radical equations?
There are several good websites to find help with radical equations. You tube has several good videos on radical equations that are free of charge.
How do you answer equations?
The answers to equations are their solutions
If a system of equations is inconsitient how many solutions will it have?
If a system of equations is inconsistent, there are no solutions.
What is the difference between a radical equation and a quadratic equation?
radical equations have sq roots, cube roots etc. Quadratic equations have x2.
Do Radical equations sometimes have extraneous solutions?
Yes, radical equations can sometimes have extraneous solutions. When solving these equations, squaring both sides to eliminate the radical can introduce solutions that do not satisfy the original equation. Therefore, it is essential to check all potential solutions in the original equation to verify their validity.
CAn someone help me with my radical equations?
There are several good websites to find help with radical equations. You tube has several good videos on radical equations that are free of charge.
What is equations that have the same solutions?
Simultaneous equations have the same solutions.
How do you answer equations?
The answers to equations are their solutions
If a system of equations is inconsitient how many solutions will it have?
If a system of equations is inconsistent, there are no solutions.
Do equations have solutions?
Equations do have solutions, sometimes they may be a little difficult to figure out.
What is the difference between a radical equation and a quadratic equation?
radical equations have sq roots, cube roots etc. Quadratic equations have x2.
What are equations that have the same answer?
Simultaneous equations have the same solutions
What reasoning and explanations can be used when solving radical equations?
The basic method is the same as for other types of equations: you need to isolate the variable ("x", or whatever variable you need to solve for). In the case of radical equations, it often helps to square both sides of the equation, to get rid of the radical. You may need to rearrange the equation before squaring. It is important to note that when you do this (square both sides), the new equation may have solutions which are NOT part of the original equation. Such solutions are known as "extraneous" solutions. Here is a simple example (without radicals): x = 5 (has one solution, namely, 5) Squaring both sides: x squared = 25 (has two solutions, namely 5, and -5). To protect against this situation, make sure you check each "solution" of the modified equation against the original equation, and reject the solutions that don't satisfy it.
How many solutions would you expect for this system of equations?
To determine the number of solutions for a system of equations, one would typically analyze the equations' characteristics—such as their slopes and intercepts in the case of linear equations. If the equations represent parallel lines, there would be no solutions; if they intersect at a single point, there is one solution; and if they are identical, there would be infinitely many solutions. Without specific equations, it's impossible to provide a definitive number of solutions.
When do you need to check for extraneous solutions?
You need to check for extraneous solutions when solving equations containing variables in denominators or within radical expressions. These solutions may arise from introducing new roots or excluded values during manipulations, which need to be verified to ensure they are valid in the original equation.
How many solutions does the system of linear equations shown have?
As there is no system of equations shown, there are zero solutions.
