# |(x^2 y^3)/(x^4+y^4 )| ≤|x|+|y|

1

2015-04-29T02:41:01+05:30

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( x² - y² )² >= 0
x⁴ + y⁴ - 2 x² y² >= 0
x⁴ + y⁴  >=  2 x² y²

(x⁴ + y⁴) |y|  >=  2 x² y² |y|  >= 2 x² y³      ---- (1)

further, we also see that  (x⁴ + y⁴) ( |y| + |x| )  >=  2 x² y³ + 2 x³ y²

Thus we see clearly that,  from  (1)

| (x² y³ ) / (x⁴ + y⁴) |  <=  |x| + |y|
The text passage contains a mathematical inequality and a proof or derivation showing that the inequality holds true. There is no explicit question or request for an answer within the text.
no_question
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# |(x^2 y^3)/(x^4+y^4 )| ≤|x|+|y|

1

2015-04-29T02:41:01+05:30

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
( x² - y² )² >= 0
x⁴ + y⁴ - 2 x² y² >= 0
x⁴ + y⁴  >=  2 x² y²

(x⁴ + y⁴) |y|  >=  2 x² y² |y|  >= 2 x² y³      ---- (1)

further, we also see that  (x⁴ + y⁴) ( |y| + |x| )  >=  2 x² y³ + 2 x³ y²

Thus we see clearly that,  from  (1)

| (x² y³ ) / (x⁴ + y⁴) |  <=  |x| + |y|
user
The text passage contains a mathematical inequality and a proof or derivation showing that the inequality holds true. There is no explicit question or request for an answer within the text.

TYPE: NO_QUESTION