How Can Algebra Help Solve Tricky Questions with Ease?

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The discussion focuses on simplifying the expression 1 + sqrt(2) + sqrt(3) + sqrt(6) by recognizing that sqrt(6) can be expressed as sqrt(2) * sqrt(3). Participants debate whether this insight aids in factoring the left-hand side or solving the overall problem. Some express skepticism about the helpfulness of the hint provided. Additionally, there are reminders about forum guidelines, emphasizing the importance of typing out problems and solutions rather than posting thumbnails. The conversation highlights the challenges of applying algebraic simplifications effectively.
Kaustubh sri
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Look at the lefthand side 1 +sqrt(2) + sqrt(3) + sqrt(6)

and recall that sqrt(6) = sqrt(2) * sqrt(3)

Does that help?

I'm not sure if my hint will help but it is a curious connection to simplify the lefthand side into factors.
 
jedishrfu said:
Look at the lefthand side 1 +sqrt(2) + sqrt(3) + sqrt(6)

and recall that sqrt(6) = sqrt(2) * sqrt(3)

Does that help?

I'm not sure if my hint will help but it is a curious connection to simplify the lefthand side into factors.

No i think it does'nt
 
Kaustubh sri said:
No i think it does'nt

so it didn't help you factor the LHS or it didn't help you with the problem as a whole?
 
Kaustubh sri said:
Question is in this way

Do not post thumbnails. Type out the problem and the solution. Read the 'pinned' thread "Guidlines for students and helpers" by Vela, which explains the reason for this policy.
 

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
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