Real number x s.t. relation is satisfied?

[r0bHadz]

Homework Statement

$\sqrt{x-2} = 3 -2\sqrt x$

Homework Equations

The Attempt at a Solution

Lang says there is no number but i found x = 2.023932257 to work when plugged into a ti84 calculator.

Am I wrong somehow? If not, can anyone tell me a book that teaches all of the same material as langs but isn't littered with errors? Look at my past 3 threads, all errors found in his book. for a book that's been praised so much I've been wasting so much time with errors and there is no error page available. I do not get why a book with so many errors per chapter is praised so much

 

[r0bHadz]

I guess maybe stewarts Calculus books have just set a standard for me that other math books just can't meet? Unless I am wron in my answer for x...

 

[PeroK]

Homework Statement

$\sqrt{x-2} = 3 -2\sqrt x$

Homework Equations

The Attempt at a Solution

Lang says there is no number but i found x = 2.023932257 to work when plugged into a ti84 calculator.

Am I wrong somehow? If not, can anyone tell me a book that teaches all of the same material as langs but isn't littered with errors? Look at my past 3 threads, all errors found in his book. for a book that's been praised so much I've been wasting so much time with errors and there is no error page available. I do not get why a book with so many errors per chapter is praised so much

If you square both sides of the equation, you'll get a quadratic in $\sqrt{x}$, from which you can get both solutions.

 

[r0bHadz]

If you square both sides of the equation, you'll get a quadratic in $\sqrt{x}$, from which you can get both solutions.

One of the solutions doesn't work

 

[Hiero]

One of the solutions doesn't work

You should remember the domain of the original equation, namely 2 ≤ x ≤ c
[edit: I really should say the domain of f(x) = sqrt(x-2) - 3 + 2*sqrt(x), the equation f(x) = 0 doesn’t have a “domain”]

When we square the equation it looks like the domain is now x ≥ 0 (in which we get two solutions) but we must remember to only allow solutions from the original domain.Nonetheless you should use PeroK’s method to find the precise solution, “2.023932257” is just an approximation.

 

[Ray Vickson]

Homework Statement

$\sqrt{x-2} = 3 -2\sqrt x$

Homework Equations

The Attempt at a Solution

Lang says there is no number but i found x = 2.023932257 to work when plugged into a ti84 calculator.

Am I wrong somehow? If not, can anyone tell me a book that teaches all of the same material as langs but isn't littered with errors? Look at my past 3 threads, all errors found in his book. for a book that's been praised so much I've been wasting so much time with errors and there is no error page available. I do not get why a book with so many errors per chapter is praised so much

No, you are right. You can solve the equation exactly by setting $y = \sqrt{x}$ and squaring the resulting equation $\sqrt{y^2-2} = 3 - 2y$. You will get a quadratic equation that has two roots for $y$, but one of them is not a valid solution to the original, un-squared equation.

 

[Mark44]

The Attempt at a Solution

Lang says there is no number but i found x = 2.023932257 to work when plugged into a ti84 calculator.

Am I wrong somehow? If not, can anyone tell me a book that teaches all of the same material as langs but isn't littered with errors? Look at my past 3 threads, all errors found in his book. for a book that's been praised so much I've been wasting so much time with errors and there is no error page available. I do not get why a book with so many errors per chapter is praised so much

Which book are you studying from? By that, I mean what is the title, publisher, and copyright date. I'm wondering if there is a newer edition with fewer of the egregious errors you've pointed out.

 

[FactChecker]

Am I wrong somehow? If not, can anyone tell me a book that teaches all of the same material as langs but isn't littered with errors? Look at my past 3 threads, all errors found in his book. for a book that's been praised so much I've been wasting so much time with errors and there is no error page available. I do not get why a book with so many errors per chapter is praised so much

One way or another, you seem to have learned enough to find the errors. Are the errors causing a great deal of trouble? There are several books with a lot of practice exercises that may have been better proofread. I always liked the Schaum's Outline series of books because of the huge number of worked and practice problems.

 

[r0bHadz]

Which book are you studying from? By that, I mean what is the title, publisher, and copyright date. I'm wondering if there is a newer edition with fewer of the egregious errors you've pointed out.

Basic Mathematics by Serge Lang, Addison Wesley Publishing Company, 1971

 

[Mark44]

Basic Mathematics by Serge Lang, Addison Wesley Publishing Company, 1971

It looks like yours is an old version. Amazon shows the same title in a 1998 edition - https://www.amazon.com/dp/0387967877/?tag=pfamazon01-20

Maybe he cleaned up some of the errors in the intervening 27 years.

 

[r0bHadz]

It looks like yours is an old version. Amazon shows the same title in a 1998 edition - https://www.amazon.com/dp/0387967877/?tag=pfamazon01-20

Maybe he cleaned up some of the errors in the intervening 27 years.

Hmm from this list:

https://www.google.com/search?q=boo.....69i57j0l2.7246j0j4&sourceid=chrome&ie=UTF-8

It appears that there is only one "Basic Mathematics" book.I guess I'll just continue to read the book and post on here if I have any questions. Still kinda disappointed but oh well. May I ask what book you used for basic math?

 

[Mark44]

It appears that there is only one "Basic Mathematics" book.

There are two editions -- one from '71 and the other from '98.

May I ask what book you used for basic math?

I don't remember, since that would have been around 7th and 8th grade back in the late 50's. I took Algebra in 9th grade, Geometry in 10th, Alg/Trig in 11th, and Calculus in 12th grade.

 

[FactChecker]

Even if it is the same edition, there will often be a page of erratum included in later printings to correct errors by the author like the ones you are finding. It is not bound in the book, but is inserted loosely in the book. In the reviews and on-line, I found comments about a few errors but I could not find anything about an erratum sheet.

PS. From what I can see, it looks like there is only one edition, but at least 3 printings. The printer may correct his own errors in the later printings.