If x and y are real numbers,which of the foll | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) By the triangle inequality for absolute values,we have the property: $||x| - |y|| \leq |x - y| \leq |x| + |y|$.Specifically,the identity $|x - y|

Vedclass · Accepted Answer

$|x - y| = ||x| - |y||$

Vedclass · Answer

(C) By the triangle inequality for absolute values,we have the property: $||x| - |y|| \leq |x - y| \leq |x| + |y|$.Specifically,the identity $|x - y| = ||x| - |y||$ is not always true for all real $x$ and $y$.However,checking the standard properties of absolute values:$1$. $|x + y| \leq |x| + |y|$$2$. $|x - y| \geq ||x| - |y||$Looking at the options provided,none of the equalities are universally true for all real $x$ and $y$. However,in many textbook contexts,the question likely intends to test the reverse triangle inequality property: $||x| - |y|| \leq |x - y|$.Given the standard form of such questions,if we assume the question implies which inequality holds or is a standard identity,there might be a typo in the options. But strictly mathematically,none of the equalities $A, B, C, D$ are identities. If we must choose the most 'standard' related property,$C$ is often discussed as the lower bound.

If $x$ and $y$ are real numbers,which of the following is always true?

Similar Questions

If $z_1, z_2$ are two complex numbers satisfying $\left|\frac{z_1-3 z_2}{3-z_1 \bar{z}_2}\right|=1$ and $\left|z_1\right| \neq 3$,then $\left|z_2\right|$ is equal to

The value of $\left| \frac{1+i \sqrt{3}}{\left(1+\frac{1}{i+1}\right)^{2}} \right|$ is

If $z \neq 0$ is a complex number such that $|z - \frac{1}{z}| = 2$,then the maximum value of $|z|$ is:

If $z = \frac{1}{1 - \cos \theta + i \sin \theta}$ and $\theta$ is acute,then the modulus and amplitude of $z$ respectively are:

Let complex number $z$ be such that $|z - \frac{6}{z}| = 5$,then the maximum value of $|z|$ will be -

Vedclass Test Series

Exam Paper Generator

Online Exam Module