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A solution to an equation that you get at the end of whatever method you use that does not actually solve the original equation. One well-known example:
1=2 ====>0=0 Therefore, one equals two.
x0 x0
The laws of algebra says that we can do this because we multiplied both sides by zero. Logically, we all know this isn't actually true. This is what extraneous solutions look like when solving linear equations:
2x+3=9 If you assume x=1... 2(1)+3=9 ...and multiply everything by 0...
0=0. Therefore, my guess is correct and x=1. <==This is extraneous
This is a minor flaw in algebra, but not like what Russel's paradox in set theory because there are explanations why this happens. Here's a more useful example of how extraneous roots occur naturally:
Solve this the way every algebra student knows, and you get x=-2. Put this back into the equation, however, and you divide by zero. -2 is an extraneous solution in this case. If the only solutions are extraneous, then the equation cannot be solved.
This is why we check rational equations: we want only actual solutions.
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Is one solution to a real-world problem involving a quadratic equation always extraneous?
No. Sometimes they are both extraneous.
What is the extraneous solution to w equals sqrt 7w?
An "extraneous solution" is not a characteristic of an equation, but has to do with the methods used to solve it. Typically, if you square both sides of the equation, and solve the resulting equation, you might get additional solutions that are not part of the original equation. Just do this, and check each of the solutions, whether it satisfies the original equation. If one of them doesn't, it is an "extraneous" solution introduced by the squaring.
What is an example of a algebra problem with no solution?
well there are two types...no solution or empty set(slashed 0) or in algebra two extraneous solutions...problems that seem to have answers but if you check they don't. its easier to give an example of the no solution: -2x-3=-2x+6 +2 +2 __________ -3 does not = 6 so there is no solution remember all variables have to cancel out and the integer cant equal each other for this to occur. if either everything including the integers canceled out or both sides equal the same then it is all real numbers. hope this helps :)
What is an extraneous solution to the equation x-3 equals sq rt 5-x?
x - 3 = √(5 - x); square both sides, for the left side use (a - b)2 = a2 - 2ab + b2 x2 - 6x + 9 = 5 - x; add x and subtract 5 to both sides x2 - 5x + 4 = 0; this is factorable since 4 = (-1)(-4) and (-1) + (-4) = -5 (x - 1)(x - 4) = 0; let each factor equal to zero x - 1 = 0; x = 1 x - 4 = 0; x = 4 Check if 1 and 4 are solutions to the original equation. 1 - 3 =? √(5 - 1) -2 =? √4 (recall the radical symbol is looking only for the positive root) -2 = 2 false, so that 1 does not satisfy the original equation, so it is an extraneous solution. 4 - 3 =? √(5 - 4) 1 =? √1 1 = 1 true, so that 4 is a solution to x - 3 = √(5 - x).
What If a system of linear equations has no solution?
It can happen. Then there is no solution!It can happen. Then there is no solution!It can happen. Then there is no solution!It can happen. Then there is no solution!
A solution that does not satisfy the original equation?
an extraneous solution.
What is a unacceptable solution called?
An unacceptable solution is an extraneous one.
What is an extraneous solution of an equation?
when you solve a questiom, you get an answer. If you chect your answer by substituting the value of the variable in the question and you don't get L.H.S and R.H.S equal then your answer is called extraneous solution.
What is a solution of an eqaution derived from an original equation that is not a solution of the original equation?
Extraneous solution
Is one solution to a real-world problem involving a quadratic equation always extraneous?
No. Sometimes they are both extraneous.
If there is no solution to a system of equations it means?
extraneous solution. or the lines do not intersect. There is no common point (solution) for the system of equation.
What does extraneous mean What must you do to determine whether a solution is an extraneous solution?
Extraneous means extra and unnecessary. Extraneous solutions are values that can arise from the process of solving the equation but do not in fact satisfy the initial equation. These solutions occur most often when not all parts of the process of solving are not completely reversible - for example, if both sides of the equation are squared at some point.
What is the extraneous solution to w equals sqrt 7w?
An "extraneous solution" is not a characteristic of an equation, but has to do with the methods used to solve it. Typically, if you square both sides of the equation, and solve the resulting equation, you might get additional solutions that are not part of the original equation. Just do this, and check each of the solutions, whether it satisfies the original equation. If one of them doesn't, it is an "extraneous" solution introduced by the squaring.
Which is the extraneous solution of -x the square root of 2x 15?
The answer would probably be either -3 or 5
What is another word for not needed?
extraneous " not pertinent; irrelevant: an extraneous remark; extraneous decoration."
What do you call the solution of a equation derived from an original equation that is not a solution of the original equation?
That's an extraneous solution. You need to check for these when algebraically solving equations, especially when you take both sides of an equation to a power.
Why is it necessary to check for extraneous solutions in radical equations?
1) When solving radical equations, it is often convenient to square both sides of the equation. 2) When doing this, extraneous solutions may be introduced - the new equation may have solutions that are not solutions of the original equation. Here is a simple example (without radicals): The equation x = 5 has exactly one solution (if you replace x with 5, the equation is true, for other values, it isn't). If you square both sides, you get: x2 = 25 which also has the solution x = 5. However, it also has the extraneous solution x = -5, which is not a solution to the original equation.
