Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

hartnn Group Title

Anyone getting bored? try this : If a³ + b³ = 0 , then the value of log (a + b) – 0.5(log a + log b + log 3) is equal to ??

  • 2 years ago
  • 2 years ago

  • This Question is Closed
  1. hartnn Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    just for safety: a\(\ne\)b a\(\ne\)-b

    • 2 years ago
  2. ParthKohli Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    \[a^3 + b^3 = (a + b)(a^2 - ab + b^2)\]So,\[(a + b)(a^2 - ab + b^2) = 0\]Dividing both sides by a + b,\[a^2 - ab + b^ 2 = 0\]Since \(a^2 - 2ab + b^2 = (a - b)^2\), we have,\[a^2 - 2ab + b^2 +ab = 0\]\[(a - b)^2 + ab = 0\]\[(a - b)^2 = - ab\]\[a^2 + b^2 = ab\]One such case is a = 0 and b = 0, but you haven't allowed that. :(

    • 2 years ago
  3. hartnn Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    hmm....nice try no other formula for a^3+b^3 ?

    • 2 years ago
  4. nipunmalhotra93 Group Title
    Best Response
    You've already chosen the best response.
    Medals 3

    Are you sure that your question is correct? If a^3 + b^3=0, then either a=-b or a=b=0.... :\ (because x^3 if a one one function)

    • 2 years ago
  5. hartnn Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    yes, question is correct.

    • 2 years ago
  6. nipunmalhotra93 Group Title
    Best Response
    You've already chosen the best response.
    Medals 3

    0

    • 2 years ago
  7. hartnn Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    how ?

    • 2 years ago
  8. nipunmalhotra93 Group Title
    Best Response
    You've already chosen the best response.
    Medals 3

    continuing from parthkohli, |dw:1347876944383:dw|

    • 2 years ago
  9. nipunmalhotra93 Group Title
    Best Response
    You've already chosen the best response.
    Medals 3

    and your question simplifies to |dw:1347876996875:dw|

    • 2 years ago
  10. mukushla Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    neat solution

    • 2 years ago
  11. hartnn Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    yes, thats right, its 0.there is easier way. rather than continuing...

    • 2 years ago
  12. nipunmalhotra93 Group Title
    Best Response
    You've already chosen the best response.
    Medals 3

    @mukushla thanks :) @hartnn what is it?

    • 2 years ago
  13. hartnn Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    \((a^3+b^3)=(a+b)^3-3ab(a+b)=0\) and the rest is ............

    • 2 years ago
  14. nipunmalhotra93 Group Title
    Best Response
    You've already chosen the best response.
    Medals 3

    haha... yeah :D

    • 2 years ago
  15. nipunmalhotra93 Group Title
    Best Response
    You've already chosen the best response.
    Medals 3

    well even though we solved it, it IS technically wrong I think? :\

    • 2 years ago
  16. nipunmalhotra93 Group Title
    Best Response
    You've already chosen the best response.
    Medals 3

    |dw:1347877692079:dw|

    • 2 years ago
  17. nipunmalhotra93 Group Title
    Best Response
    You've already chosen the best response.
    Medals 3

    |dw:1347877816341:dw|

    • 2 years ago
  18. hartnn Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    if i read it correctly, there exist no a,b not equal to 0, such that a^2+b^2-ab = 0.....??

    • 2 years ago
  19. nipunmalhotra93 Group Title
    Best Response
    You've already chosen the best response.
    Medals 3

    Yea...to be clearer, I mean that a^2+b^2-ab=0 iff a=b=0

    • 2 years ago
  20. hartnn Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    u sure about a^2+b^2-ab=0 iff a=b=0 ?

    • 2 years ago
  21. nipunmalhotra93 Group Title
    Best Response
    You've already chosen the best response.
    Medals 3

    yea... you can try that... you won't find any a, b s.t a,b are not both zero and the condition is satisfied....

    • 2 years ago
  22. nipunmalhotra93 Group Title
    Best Response
    You've already chosen the best response.
    Medals 3

    algebraically, x^3, is a one one function... so, a^3 +b^3=0 implies a^3=(-b)^3 which implies a=-b

    • 2 years ago
  23. hartnn Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    a^3 =-b^3 have 3 roots.....i think

    • 2 years ago
  24. nipunmalhotra93 Group Title
    Best Response
    You've already chosen the best response.
    Medals 3

    Graphically,

    • 2 years ago
    1 Attachment
  25. nipunmalhotra93 Group Title
    Best Response
    You've already chosen the best response.
    Medals 3

    I plotted two graphs.... z=xy and z=x^2+y^2 they intersect only at (0,0) Yes there are three values of b for every a. But they are complex.

    • 2 years ago
  26. nipunmalhotra93 Group Title
    Best Response
    You've already chosen the best response.
    Medals 3

    If your question covers complex numbers, then it's fine.... but for real, this is it :)

    • 2 years ago
  27. nipunmalhotra93 Group Title
    Best Response
    You've already chosen the best response.
    Medals 3

    @hartnn Thanks for the time man.. that was a good exercise for me ^_^

    • 2 years ago
  28. hartnn Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    hmm..log of complex numbers....didn't think of it b4 posting....and thanks to u for wonderful explanation.

    • 2 years ago
  29. nipunmalhotra93 Group Title
    Best Response
    You've already chosen the best response.
    Medals 3

    you're most welcome buddy!

    • 2 years ago
    • Attachments:

See more questions >>>

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.