Prove that for any two real numbers x,y with x!=0 2y <= (y^2)/(x^2)+x^2

Hana Buck 2022-09-23 Answered
Prove that for any two real numbers x , y with x 0
2 y y 2 x 2 + x 2
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (2)

Kaiden Stevens
Answered 2022-09-24 Author has 12 answers
Hint:
Explore the following expression ( x y x ) 2
Did you like this example?
Subscribe for all access
mundocromadomg
Answered 2022-09-25 Author has 3 answers
By AM-GM we obtain:
y 2 x 2 + x 2 2 y 2 x 2 x 2 = 2 | y | 2 y .
Done!
Did you like this example?
Subscribe for all access

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2021-02-11

Solve the equation

32x

asked 2022-09-25
How can I prove that this function is bounded using the given hint?
f ( x ) = 1 2 sin x 1 + cos 2 x ,
Hint:
1. | A + B | | A | + | B | ,
2. | sin x | 1.
asked 2021-10-15
perform the indicated operations and express the answers in simplified form.
(11x3)2(6x+5)3
asked 2022-06-14
Fraction confusion
I read in a set of memoranda that if b x x = b a , then
x = a b a + b
How is this true? I tried working it out but I could not understand. Please help.
asked 2022-06-07
What exactly goes raising a number to a fraction mean?
I apologise for asking something so fundamental, but what exactly does
2 2 5
actually mean? I get raising a whole number to another whole number
x y
means you are multiplying x with itself y times, but what does it mean when y is a fraction?
asked 2021-09-15

Express 111 as a repeating decimal, using a slash to indicate the repeating digits. What are the decimal expansions of the following fractions: 211,311,911 and 1111?

asked 2022-08-18
How to solve this proportion
Okay I think I'm just having a major brain block, but I need help solving this proportion for my physics class.
6.0 × 10 6 x 2 = 2.0 × 10 6 ( x 20 ) 2
What's confusing me is the solution manual to this problem lists writing the proportion as,
( x 20 ) 2 x 2 = 2.0 × 10 6 6.0 × 10 6
and then proceeds to solve the problem from there... but that doesn't seem right to me. Usually you would cross multiply a proportion and solve, but they seemed to do some illegal math or something. Could you guys work me through how to solve this? This answer is 47 by the way.

New questions