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

Hana Buck

Hana Buck

Answered question

2022-09-23

Prove that for any two real numbers x , y with x 0
2 y y 2 x 2 + x 2

Answer & Explanation

Kaiden Stevens

Kaiden Stevens

Beginner2022-09-24Added 12 answers

Hint:
Explore the following expression ( x y x ) 2
mundocromadomg

mundocromadomg

Beginner2022-09-25Added 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!

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