in-3-38-solve-each-equation-for-the-variable-check-and-write-the-solution-set-3-sqrty1

Question

In $3-38,$ solve each equation for the variable, check, and write the solution set.
$$
3-\sqrt{y}=1
$$

Nick Johnson · Accepted Answer

Yeah, the equation three minus the square root of why is equal to one. That&#x27;s first. Let&#x27;s move all our constance toe one side of the equation. Let&#x27;s go ahead and subtract three. Let&#x27;s subtract three from both sides so we&#x27;ll just leave on minus three for minus 30 So zero minus squared of why that&#x27;s minus the square root of why is equal to a one minus three. What? One minus three is negative. Two. Okay, Now to sell for Why wasn&#x27;t I have negative? Describe it of why I can go ahead. I can divide or multiply both sides by a negative one to just basically change the signs. So I want to buy my negative one. Um right. Everything here I get that square root off. Why is equal to a positive two? And then it wasn&#x27;t have a square root of why I can go ahead and square both sides because the square root of why squared is equal toe. Why so, therefore, why is equal to two squared or two times two, which is for so once again. Here we see that Why is he could before meaning our solution set is set containing just the number for all right. Take care

Martha Richards · Answer

we&#x27;re going to solve this equation checker answer and then provide the solution set. So when I have the radical, isolated Aiken Square, both sides and I get three minus y on the left and once weird is one. And then I will add y over here and I get three equals a Y plus one, then also tracked one from both sides. And I get that why is equal to two? And so then, if I want to plug this back in here, I will start with my original equation. I get three minus to the square root of that is equal to one. And when I take three minus two, that&#x27;s one. So the square root of one Z equals one and here square, or the one is indeed equal to one. So this checks out. So the solutions that here, for the above equation, is for why equal Thio, too

Martha Richards · Answer

we are going to solve this equation, check our answer and then provide the solutions that so this radical is isolated. So I will square both sides. I get why squared is equal to Y plus two, and then I&#x27;ll put all of these over to one side. I&#x27;ll keep the y squared positive sort. If I subtract a wind subtracted too on both sides, then I&#x27;m going to factor this. So when I factor this, I know that these have to be wise because when I do the foil first, remember why times why gets me back to y squared? And now if I have a negative here, I have to have one positive and one negative because you can&#x27;t multiply two signs that are the same times each other and get a negative number. So negative times a positive or a positive tons and negative. It&#x27;s going to get me to this negative. And then there is only one set of factors for 22 and one. I end up with the negative here when I when I take the difference. So the two has to be the bigger number, and the one goes over here. So now solving. For this, I get why plus one is equal to zero. So that means that Y is equal to a negative one. And then I get why minus two equals zero. So I get why is equal to two. So now let&#x27;s plug those back into the original equation and see whether or not that&#x27;s gonna work out. So first I have the negative one. If I put a negative one, and for why, then take the square root of negative one plus two. I get a negative one plus two is one, and so when I take the square would have won. I get one, and one is not equal to a negative one. So this one here is not a part of the solution. Set. Let&#x27;s try plugging the two back in. So if I get a two is equal to the square root of two plus two and I have two. And two plus two is four the square root of four, and the square root of four is too. So this one does check out. So our solution set for this equation here is for when y is equal to two

Nick Johnson · Answer

we have four times the square root of why is equal to 12. So to go ahead and so on for why we can first, what we have, we have a coefficient right before we have four times the square root of why shouldn&#x27;t go ahead and can divide through by four because what 44 is just one. So therefore we just get the square root of why all the fourth one Those cancel out comes one time to square with Why, which is the square root of why is equal to well 12 divided by four is well three. Okay, so now we have the square root of Why is secretive three. We can go ahead and square both sides So we square the left side and we square the right side in the square root of Why squared just undone does the square root I would just get why So we get that why is equal to three square, which is three times three, which is equal to nine. So therefore are Andrew here is why is equal to nine and therefore our solution set is the set containing nine which would write like this We have a set. Um Kenny Mac, there&#x27;s our solution set

Martha Richards · Answer

we&#x27;re going to solve this equation, check our answer and provide a solution Set. So when I have the radical isolated, I could just square both sides. So on the left, I get four white and 12 squared is equal to 1 44 I divide both sides 54 and I get that. Why is equal to 36 when I plug this back into the original equation? Four times 36 square root of that I get square root of 1 44 is equal to 12 in the square root of 1 44 is 12 and so this does check out. So my solution set for the above equation is for when y is equal to 36.

Nick Johnson · Answer

having equation here. One plus the square root of X is equal to three. So on the left side of the equation, I have two terms, right? I have one in the square Durex. So I have an ex term and have a constant. Let&#x27;s go ahead and move. All are constants toe one side of the equation by just subtracting one from both sides. Track one from both sides. One minus 10 I just get zero plus bread of expert justice. Square root of acts is equal to three minus one squared of access equal to two and then the south for X because I have the square root of X Aiken Square, both sides to undo the square root is the square root of X squared is equal to X, and then we square both sides so excessively could the two square or two times two, which is equal to four so X secretive form, meaning that our solution set contains just the number of four. There&#x27;s our solutions said All right,

Problem

In $3-38,$ solve each equation for the variable, …

Problem 13 Easy Difficulty

In $3-38,$ solve each equation for the variable, check, and write the solution set.
$$
3-\sqrt{y}=1
$$

Answer

$\{4\}$

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$\{4\}$

Algebra 2 and Trigonometry

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Ann Xavier Gantert

Algebra 2 and Trigonometry