Prove that: |x| + |y| ≤ |x + y| + |x − y|.
Answer
Answers can only be viewed under the following conditions:
- The questioner was satisfied with and accepted the answer, or
- The answer was evaluated as being 100% correct by the judge.

4.8K
-
Leave a comment if you need any clarifications.
-
1) 2∣x∣+2∣y∣ => why do you multiplay it by 2? I mean why are you allowed to do it? 2) ∣x+x∣+∣y+y∣ =∣x+y+x−y∣+∣y+x+y−x∣ => i dont understand this step... 3) ∣x+y∣+∣x−y∣+∣x+y∣+∣y−x∣=2∣x+y∣+2∣x−y∣ => i dont know, where the ∣x+y∣+∣y−x∣ comes from but i understand that the left side would be the right side. I can see why the rest is true. My biggest problem is, why what you wrote is the conclusion of "Using triangle inequality we have ".
-
I added a note in my solution to emphasis where we exactly use the triangle inequality. Multiplication by 2 is just a trick that helps us to prove what we want.
The answer is accepted.
Join Matchmaticians Affiliate Marketing
Program to earn up to a 50% commission on every question that your affiliated users ask or answer.
- answered
- 874 views
- $4.92
Related Questions
- Artin-Wedderburn isomorphism of $\mathbb{C}[S_3]$
- Find $\lim _{x \rightarrow 0} x^{x}$
- Find $x$ so that $\begin{pmatrix} 1 & 0 & c \\ 0 & a & -b \\ -\frac{1}{a} & x & x^2 \end{pmatrix}$ is invertible
- Please help me with this math question
- Certain isometry overfinite ring is product of isometries over each local factor
- Linearly independent vector subsets.
- Algebra Question 3
- Algorithm for printing @ symbols