ProphetesAI is thinking...
extraneous
MindMap
Loading...
Sources
extraneous
extraneous, a. (ɛkˈstreɪnɪəs) [f. L. extrāne-us external (f. extrā outside) + -ous. (Cf. strange, ad. OF. estrange:—L. extrāneus.)] 1. a. Of external origin; introduced or added from without; foreign to the object in which it is contained, or to which it is attached.1638 A. Read Chirurg. ix. 67 Such...
Oxford English Dictionary
prophetes.ai
Extraneous and missing solutions
Extraneous solutions: rational
Extraneous solutions can arise naturally in problems involving fractions with variables in the denominator. Therefore, the solution x = –2 is extraneous and is not valid, and the original equation has no solution.
wikipedia.org
en.wikipedia.org
extraneous
extraneous/ɪkˈstreɪnɪəs; ɪk`strenɪəs/ adj~ (to sth)1 not belonging to or directly connected with the subject or matter being dealt with 与正题无关的 extraneous information 无关的消息 extraneous material in a book 书中的题外资料.2 coming from outside 来自外部的; 外来的 extraneous interference 外来的干涉.
牛津英汉双解词典
prophetes.ai
Extraneous solutions of radical equations - Khan Academy
The solution x = -8 is extraneous to the original equation √ (4x + 41) = x + 5. However, it is the solution to the equation -√ (4x + 41) = x + 5. The expression under the radical is same in both equations, so in terms of keeping the radicand non-negative, the value -8 is OK. If we take the function y = √ (4x + 41), then -8 would be a ...
www.khanacademy.org
Extraneous solutions (video) | Equations | Khan Academy
Extraneous solutions are values that we get when solving equations that aren't really solutions to the equation. In this video, we explain how and why we get extraneous solutions, by understanding the logic behind the process of solving equations. Questions. Tips & Thanks.
www.khanacademy.org
Extraneous solutions. I just learned of extraneous solutions on the internet and thought, "could you both lose and gain solutions in one equation?" I think that, yes, you should be able to do that. However I haven't b...
I'm not exactly sure what you mean, but sometimes it makes life easier to multiply an equation by $1$ and thus "both gain and lose a solution", like so: if $f$ is a polynomial (over $\mathbb{R}$, say), then consider $$\begin{align}f(x)&=\frac{x-a}{x-a}f(x)\\\ &=1\cdot f(x) \\\ &=f(x)\end{align}$$ fo...
prophetes.ai
Is this an extraneous solution? Does $$\sqrt{2x} = \sqrt{5x+3}$$ have an extraneous solution which is $-1$ or is the solution $-1$ ? As I solved, both sides become $\sqrt{-2}$ but negative numbers can't be in the squa...
Generally, we would say this is an extraneous solution.
prophetes.ai
Extraneous solutions to simple equations I had an interesting thought during my procrastination: is it legal to take an equation, say > $3 = a * b * c$ and do the following: > $3 = abc$ > $0 = abc - 3$ > $0 ...
When you divide by $c$, you should find that
$$0 = 1 - 3/a/b/c$$
not
$$0 = 3/a/b/c$$
So there's no extraneous solution introduced.
prophetes.ai
How is this an extraneous solution? Let's say we've got $\sqrt{4-3x} = x$. Now let's say we have $x = 1,-4$. Let's punch $-4$ in first. We wind up with $\pm4 = -4$. > How is this an extraneous solution, but pluggi...
Ok, here's the thing. A square root, when placed by itself, isn't negative, unless you put a "minus" in front of it. However, if your original equation was $x^2 = 4-3x$, both solutions would work. The confusion here arrives from you believing that $\sqrt{16}$ can be both positive and negative. Unles...
prophetes.ai
extraneous perils in Chinese - English-Chinese Dictionary | Glosbe
一般附加险 UN term Show algorithmically generated translations. Automatic translations of "extraneous perils" into Chinese . Glosbe Translate Google Translate Add example Add Translations of "extraneous perils" into Chinese in sentences, translation memory . Declension Stem .
glosbe.com
asymptote vs extraneous values I am having trouble understanding the difference between a rational function with an asymptote versus having extraneous solutions. What is the difference between the two, if there is. Ar...
An extraneous solution to a rational equation is traditionally one that will result in a hole. $\dfrac{x^2-4}{(x-2)^2}=0$ has both an asymptote and an extraneous solution at $x=2$.
prophetes.ai
Where is the step that caused the extraneous solution? $$x^{1/3}+x^{1/6}-2=0\iff (x^{1/6}-1)(x^{1/6}+2)=0$$ $\iff x^{1/6}=1$ or $x^{1/6}=-2$ $\implies x=1^6=1$ or $x=(-2)^6=64$ By checking when $x=64$:$\sqrt[3]{64}+...
An even root cannot have negative values so the solution $\sqrt[6]{x}=-2$ is not valid in $\mathbb{R}$
prophetes.ai
How to know if there is a extraneous solution in a radical expression I was trying to solve this problem: $$\sqrt{3x+13} = x+ 3$$ So I was pretty confident about this problem and started solving: $$(\sqrt{3x+13})^2...
You don't need to plug in values, if you always ensure not to add extraneous solutions.
prophetes.ai
Avoiding extraneous solutions When solving quadratic equations like $\sqrt{x+1} + \sqrt{x-1} = \sqrt{2x + 1}$ we are told to solve naively, for example we would get $x \in \\{\frac{-\sqrt{5}}{2},\frac{\sqrt{5}}{2}\\}$...
If you ensure that $$ \begin{cases} x+1\ge0\\\ x-1\ge0\\\ 2x+1\ge0 \end{cases} $$ then you can square both sides, because they are guaranteed to exist and, when $a,b\ge0$, $a=b$ if and only if $a^2=b^2$. The conditions above are equivalent to $x\ge1$. Squaring we get $$ x+1+2\sqrt{x^2-1}+x-1=2x+1 $$...
prophetes.ai
Extraneous Solutions How would I solve the following inequality algebraically? I can see the solution graphically, but I'm wondering if someone can describe the extraneous solution part algebraically. $x-7 < \sqrt{x}+3$
Let $t=\sqrt{x}$. Then we have $$t^2-7<t+3\implies t^2-t-10<0, t\geq0$$ Solving, we get \begin{align} t^2-t-10&<0\\\ \left(t-\frac12\right)^2-\frac{41}4&<0\\\ \left(t-\frac12\right)^2&<\frac{41}4\\\ \left|t-\frac12\right|&<\frac{\sqrt{41}}2\\\ -\frac{\sqrt{41}}2<t-\frac12&<\frac{\sqrt{41}}2\\\ \frac...
prophetes.ai