Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

meli1594

  • 2 years ago

What are the max and min possible values of x2 + y 2 if x+y =1 and x and y are nonnegative? What inequality between x2 + y 2 and (x+y)2 does this yield that holds for arbitrary non-negative numbers x and y?

  • This Question is Open
  1. Jonask
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[(1)^2=x^2+2xy+y^2\] \[x^2+y^2=1-2xy\] min

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

    \[-2y-2x=0\] \[x=y\] max 1/2 min ?

  3. Stacey
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Because x+y=1 and the variables cannot be negative \[0 \le x \le1\]\[0 \le y \le1\]Also y=1-x, so \[y^{2}=(1-x)^{2}=1-2x+x ^{2}\]Substitute that into your first equation to obtain \[1-2x+2x ^{2}\]Graphing this with the domain or using the derivative, you should be able to find the max and min.

  4. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

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.