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Why must all possible solutions for radical equations must be checked?
Wiki User
∙ 7y ago
This is not true. Squaring any number gives only one solution. (-4)^2 will always be 16. It will never be anything else.
Radical equations must be checked because squaring both sides can give you two completely different solutions. If you don't check it, you could end up with an incorrect answer. See this website for more information -
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This is not true. Squaring any number gives only one solution. (-4)^2 will always be 16. It will never be anything else.
Wiki User
∙ 7y ago
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What is the radical equation 4 equals x2-2-x?
It is a quadratic equation and can be rearranged in the form of:- x2-x-6 = 0 (x+2)(x-3) = 0 Solutions: x = -2 and x = 3
Sin2x - radical 2 cosx equals 0?
Sin2x = radical 2
How do you describe how to translate the graph y equals radical x to obtain the graph of each function?
You can move it up or down by adding a constant, call it c. Let c>0 Y=radical(x)+c move it up c and y= radical(x)-c moves it down c. You can move it to the right by subtracting c inside the radical sign. Let c>0 y=radical (x-c) moves it to the right c units. y=radical (x+c) moves it to the left c units.
How do solve a composite function that is a radical inside of a radical?
By radical, I am assuming that you mean square root, not cube root, quartic root, or otherwise. If this is the case, then we can use fractional exponents to help. Change sqrt(x) to x^(1/2), or x to the one half power. Then we take a radical of a radical which becomes sqrt(x^(1/2)) = (x^(1/2))^(1/2) = x^(1/4). When we raise a power to a power, we multiply exponents. So the answer to the square root of the square root of x is x to the one fourth power, or the 4th root of x.
What is x times radical x?
x√x=x^1.5
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 the difference between a radical equation and a quadratic equation?
radical equations have sq roots, cube roots etc. Quadratic equations have x2.
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.
Do all quadratic equations have two solutions?
I may only be in 8th grade but I am absolutely positive that all quadratic equations have 2 solutions. No - They may have 0,1, or 2 answers For example, the problem x^2 + 8x +16 = 0 has only one solution -4. This is because the radical evaluates to 0 rendering the +/- sign irrelevant.
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.
In general when solving a radical equation should you first isolate the radical and then both sides?
It often helps to isolate the radical, and then square both sides. Beware of extraneous solutions - the new equation may have solutions that are not part of the solutions of the original equation, so you definitely need to check any purported solutions with the original equation.
Why do you have to check the solutions when you have to solve radical equations?
Checking your solution in the original equation is always a good idea,simply to determine whether or not you made a mistake.If your solution doesn't make the original equation true, then it's wrong.
Why do you check your answers for rational equations and radical equations?
You plug the number back into the original equation. If you have a specific example, that would help.
How do you solve radical equations with variables on both sides?
First, get the radical by itself. Then, square both sides of the equation. Then just solve the rest.
How is solving radical equations similar to solving linear equations?
It really is utilized to solve specific variablesIt really is utilized to rearrange the word.
Why is the radical a2 b2 is not equal to a b?
Because a radical has two solutions, the positive and negative. This means that √(a2b2) has twice as many solutions as ab. ab is in fact a subset of √(a2b2).
How is a radical equation similar to a linear equation?
Technically,no. A radical equation has a radical (Square root) in it, and has two solutions because the square root can be positive or negative.
