(Algebra) I'm looking at a solution to an Intro Real Analysis problem, but there's a simple algebraic step being made in the solution that I don't get. It seems like they're multiplying by the conjugate of something, but not quite. Prompt below.

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions.

A community for students.

(Algebra) I'm looking at a solution to an Intro Real Analysis problem, but there's a simple algebraic step being made in the solution that I don't get. It seems like they're multiplying by the conjugate of something, but not quite. Prompt below.

Mathematics
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions

Problem one on page one: http://www.math.cornell.edu/~mionescu/Teaching/Spring2008/prelim2_311_sol.pdf I don't understand what is happening when they get the expression of n's in absolute values that is less than epsilon that becomes the conjugate and the reciprocal of what it previously was?
I'd like to say they just multiplied (a-b) time (a+b) on top and bottom, but I don't see how that would lead to the given result.

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

\[ \sqrt{n+1}-\sqrt{n}<\epsilon\\ \left(\sqrt{n+1}-\sqrt{n}\right)\left(\sqrt{n+1}+\sqrt{n}\right)<\epsilon\left(\sqrt{n+1}+\sqrt{n}\right)\\ n+1-n<\epsilon\left(\sqrt{n+1}+\sqrt{n}\right)\\ 1<\epsilon\left(\sqrt{n+1}+\sqrt{n}\right)\\ \frac{1}{\sqrt{n+1}+\sqrt{n}}<\epsilon \]
\[ (a+b)(a-b)=a^2-b^2 \]
And this does not look like an introductory course to analysis.

Not the answer you are looking for?

Search for more explanations.

Ask your own question