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In $3-38,$ solve each equation for the variable, check, and write the solution set.$$\sqrt{x+4}-\sqrt{x-1}=1$$

$\{5\}$

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Chapter 3

REAL NUMBERS AND RADICALS

Section 8

Solving Radical Equations

Whole which of Numbers

Fractions and Mixed Numbers

Decimals

04:36

In $3-38,$ solve each equa…

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00:57

03:39

02:28

02:49

06:13

04:23

03:18

04:33

here We have immigration. The square root of X plus four minus the square root of X minus one is equal to one. So well, if we were to Hmm. Let's see. How about if we add, um, a square root of X minus one to both sides, So that would then give us the square root of X plus four within the equal to well, one plus the square root of X minus one. Why do we do this? But now we go ahead and square both sides. Square in the left side is just going to give us X plus four, right? The squarely of plus four square is just equal to X plus four. So but the right side we have what? One plus the square root of X minus one. So we square the right side we get while we get one plus the square root of X minus one times, right. One plus the square root of X minus one times itself. But the needs to square it Well, this was gonna equals one times. One is one. Then we get one time squid of X minus one stashed a squirt of X minus one plus right, Um, plus another one times the square X minus one that's gonna give us while plus two times the square root of X minus one on Ben while X minus one times X minus one just gives us X minus one so that we get while plus, um plus X minus one. So plus X minus one. Okay, so squaring the left side again, the squid of X plus four squared Just could just x plus four. So we get X Plus four is gonna be equal to again squaring This gives us this year's We get one plus two times the square root of X minus one, uh, plus X minus one. Okay, well, the exes are gonna cancel out right track action. Both sides and the exes are gone. Um, And then, well, we can go ahead and we can add one to both sides. Um, well, actually, not really. Because you have a one minus one. So that's gonna have to cancel. It becomes zero. Okay, so let me get well, just a four is equal to two times the square root of X minus one, right. That's what this is gonna basically simplify down too. And then we can go ahead and divide through by two to get for over two or just two is equal to the square root of X minus one. And now we can go ahead and square both sides to eliminate this square root, so squaring both sides now gives us while two square is four is equal to just X minus one. So adding one the both sides gives us that X right is equal to five. So we have that X is equal to fight, right? Just adding one to both sides. You have exercise five. Now go ahead and check the solution in our original equation. Here is this true or the square root of five plus four is just the square root of nine and then we have minus, while the square root of five minus one that's the square root of four that should be equal toe won with a score of nine is three, and a squirt of four is to just have three minus two, which indeed is equal to one writes that simplifies down to one. Is it with the one of hat is true that checks out and therefore our solution here. X equals five is a balance solution in our solution set is the set containing just the number of five. All right, take care.

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