explain-why-sqrtx30-has-no-solution-in-the-set-of-real-numbers-while-sqrtx3-geq-0-is-true-for-all-re

Name: explain why sqrtx30 has no solution in the set of real numbers while sqrtx3 geq 0 is true for all re
Uploaded: 2020-08-14
Duration: 2 min 47 s
Channel: Numerade
Description: Explain why $\sqrt{x+3}<0$ has no solution in the set of real numbers while $\sqrt{x+3} \geq 0$ is true for all real numbers greater than or equal to $-3 .$

Question

Explain why $\sqrt{x+3}<0$ has no solution in the set of real numbers while $\sqrt{x+3} \geq 0$ is true for all real numbers greater than or equal to $-3 .$

Nick Johnson · Accepted Answer

first that consider this inequality. The square root of X plus three is less than zero. So this is gonna have no solution, No solution in the Rio numbers, right? So no solution for, um for X such that X is an element of the real numbers. This is the same. That right? There&#x27;s no X. That&#x27;s a real number. Such that X is a solution to this. Why? Well, what do we know about the square? Root was under the square root right? Cannot be negative. It&#x27;s under the square root. Can be. If if this was negative. If X plus three was negative, then while we&#x27;d be undefined in the real numbers, right, we haven&#x27;t imaginary number. So the domain of this, if it was a function, well, the smallest actually could possibly put in here would be negative. Three, right. Anything less than negative three. And you add three to it. You&#x27;re gonna be negative. So the smallest execute possibly put in here. That makes sense. A two part of the domain would be negative. Three or negative. Three plus three is equal to zero. And anything larger than negative three, right? This is always gonna be great and zero So X plus three the square root of experts three can never be less than zero. Never look at this Inequality squared of experts. Three is greater than or equal to zero. This is true for all X, right, Because again, this small is actually possibly put in here. That&#x27;s part of domain would be negative. Three, right? And native three is equal to zero. So this will be true and then any greater value, right? Any value of X greater than three while then the square root of X plus three is going to be positive. It&#x27;s going to be great in zero. So then this would always be true for any possible acts you put in here any real number value of X. So the first inequality right is has no solution for any extra go number because the smallest actually could put in is negative. Three, right. Native three plus three is zero. So which is not less than zero, and any bigger X is not gonna be less than zero. But for any part, any possible acts in the domain again, the domain is while X must be, um, must be greater than or equal to negative three. Right? That&#x27;s the domain. And then this second inequality right. The square root of X plus tree will always be greater than or equal to zero for all acts in the domain. All right, let&#x27;s explain too much, but then they sense.

Deandre Johnson · Answer

all right for this problem were asked to explain why these two any qualities do not have the same solutions. Now, there&#x27;s many ways to go about explaining this, but I&#x27;m really gonna focus on this X minus three factor that&#x27;s in both of so to the left. In this rational expression, we see that if X is equal to three, the denominator equals zero. And if the denominator equals zero, then that makes the entire expression undefined. So really ex cannot equal three over here in this rational expression. Now, if we look over here to this quadratic inequality, we see that if X equals three, then the entire expression is equal to zero, which is which is okay because we&#x27;re looking for values of X that make the function greater than or equal to zero. So to the right, X equals three satisfies the solution set while to the left. X equals three does not satisfy the solution said so these two inequalities cannot have the same solutions by the simple fact that the left one does not include three and the right one does include three

Mitchell Cutler · Answer

all right. We look at X plus two different height because minus three, it&#x27;s greater than zero and past your times X minus three. It&#x27;s scripted than zero. Why are these two questions went out? The simple solutions well, they&#x27;re gonna equal was your or equal. Let&#x27;s see, Let&#x27;s take a look at this rate one first. So no, it was your one X. Is it what, you figure two or positive? Three. And on this left equation with X is equal to negative two. Um, that records your benefits equal to, um, people to need a three, which it can&#x27;t really be. You kind of got, uh, this problem right where we&#x27;re dividing by zero. So that is, um, going to cause a problem in our ingredients. Who? That&#x27;s kind of these two, um, points needed to end. Bruce, that supports your positive three. What equations? Where? Um, that&#x27;s equal to zero. And that will be the same. Um, how the same truth values. Um, between those two points

Amy Jiang · Answer

Okay, so let&#x27;s start by squaring both sides so we see that X is equal to one. Now, if we plug in exit acquits to one into original equation, we see it out. The square root of one is equal to negative one, and one is equal to negative one. And since these two are not true, this is actually a extraneous solution.

Ankit Gupta · Answer

do. An equation is squared off. X is equal minus one. No, that&#x27;s where Ah, a negative number. There&#x27;s no exist health equation as no solution.

Anna Jones · Answer

So for this problem, if its simplest way that we can consider why this equation will never be true is to think about the value of the values of the square root of X function. So you may have seen that this is called a parent function somewhere along the way. But when we think about just the square root of X equals why we know that there&#x27;s some parameters. Eso this graph if I draw just a rough sketch of it is all in that first quadrant, meaning that X is always greater than or equal to zero, and why is always greater than or equal to zero? And so the given equation has the radical oven expression plus the radical oven expression equal to negative one. And we simply know that this can never happen, because the outputs of a square root function are never less than zero. Eso a radical will never give us an output of a negative number. And so that is why that this expression will never work

Problem

In Example $3,$ are $x-1=\sqrt{15-7 x}$ and $(x-1…

Problem 1 Easy Difficulty

Explain why $\sqrt{x+3}<0$ has no solution in the set of real numbers while $\sqrt{x+3} \geq 0$ is true for all real numbers greater than or equal to $-3 .$

Answer

See explanation.

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