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Concept Check Study this incorrect "solution." WHAT WENT WRONG?$$\begin{aligned}2(x-1)^{2}-3(x-1)+1 &=0 \\2 u^{2}-3 u+1 &=0 \\& \text { Let } u=x-1 \\(2 u-1)(u-1) &=0 \\2 u-1=0 & \text { or } u-1=0 \\u=\frac{1}{2} & \text { or } \quad u=1\end{aligned}$$Solution set: $\left\{\frac{1}{2}, 1\right\}$

Precalculus

Algebra

Chapter 11

Quadratic Equations, Inequalities, and Functions

Section 4

Equations Quadratic in Form

Introduction to Conic Sections

Equations and Inequalities

Functions

Polynomials

McMaster University

Harvey Mudd College

Baylor University

Lectures

01:43

In mathematics, a function…

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04:15

Concept Check Study this i…

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Explain the mistake that i…

09:34

Determine the solution set…

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Work with a group to exami…

00:53

07:43

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Use $A^{-1}$ to find the s…

03:20

$\begin{aligned}(1-i) x_{1…

00:17

If $\cos x=\frac{1}{3},$ f…

01:51

The following steps appear…

02:18

Explain the error in the f…

00:54

In Exercises, explain the …

00:38

06:12

Solve each equation. Check…

01:54

01:13

01:02

What is wrong with the beg…

03:51

For Problems $21-26,$ use …

Okay, So way have walked choo times. The quantity X minus one squared minus three. Have the quality X minus one plus one is equal to zero. So the word we see here we say that let you just let you be let you be people to while X minus one. All right. To be just a fine and variable here to be equal to X minus one. Well, then we basically just get a quiet drink. Okay? Instead of two times this quantity squared, we just get to times you square and then minus three while just three times you and then plus one is equal to zero. Okay? And then from here, what we do next is we factor, right? Well, so that's part a good next step. We factor this thing and they say this factors as, um to you, Minus one times U minus one and next to equal to zero, right? Is this tractor correctly? Well, yeah. You can always distribute here, and this is to you times you used to You square and get minus two U minus one. Use that's minus two U minus. U minus three. You and minus one times minus one plus one. So, yeah, that's factored right now, we have two factors, right that are multiplied together, equal to zero. So this means that either two U minus one is equal to zero or u minus one is equal to zero. Okay. And then we say that we have to. You minus one is equal to zero. That means that to you is even a one. So therefore, you is equal to 1/2 okay? Or what you might is what is equal to zero. That means that you is equal to one. No, we see what went wrong. Because one of these answers is actually not correct. So it looks like, right every step we did was totally valid, which it waas. Okay, What we end up with is an extraneous solution. So is it actually check these answers back in our original equation. Now, if you check 1/2 that 1/2 minus one squared times to, um, get well, 1/2 Indian minus. Um, Do you want half minus one times minus three? Get by. That's what, 1.5 to 1/2. Minus 1.5 of negative. One plus one equals zero. Okay, so you can check that and see that? Well, 1/2 actually works. But if you put in one well, ones actually easier to check if you put in one. What happened? I have one month is one that zero. So zero square times to I don't care zero kind Anything is the office first? Sure of is zero. The second term is also zero, right? Because I'm playing in one for X. So one minus 10 Thanks. Later. Three. That's still 00 minus 000 plus one. That's one we're saying that one is equal to zero. Well, that's not true. So you was equal to one is not a solution, right? It's an extraneous solution. And what was what went wrong here? Is that wealth ever solve this right? Celtic pretty much correctly. But then did not go ahead. It did not check. Um, both solutions to make sure they actually solved the original creation. Because U equals one does not make this equation true. So u equals one or one. Well, in this case, X equals one. We actually, we switched S o u u equals one. You actually does right solve. Um, if you plug in one for you, right. You do get, um you know, So you it was one. Makes the equations with you. True, but it does not make you quit. The original equation was for X, so if every made a substitution to sell this, which was a good step and it got us the right answer view was 1/2 But we got extraneous solutions. We did not go and check the answer of one in for X in our original equation. Okay, Digger.

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