If a = frac{x}{y-z},b = frac{y}{z-x},and c = | vedclass

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

Question

(B) Given $a = \frac{x}{y-z}$,$b = \frac{y}{z-x}$,$c = \frac{z}{x-y}$.Let us test with values $x=1, y=2, z=4$ (ensuring denominators are non-zero).$a

Vedclass · Accepted Answer

-$1$

Vedclass · Answer

(B) Given $a = \frac{x}{y-z}$,$b = \frac{y}{z-x}$,$c = \frac{z}{x-y}$.Let us test with values $x=1, y=2, z=4$ (ensuring denominators are non-zero).$a = \frac{1}{2-4} = -\frac{1}{2}$$b = \frac{2}{4-1} = \frac{2}{3}$$c = \frac{4}{1-2} = -4$Now calculate $ab + bc + ca + abc$:$ab = (-\frac{1}{2})(\frac{2}{3}) = -\frac{1}{3}$$bc = (\frac{2}{3})(-4) = -\frac{8}{3}$$ca = (-4)(-\frac{1}{2}) = 2$$abc = (-\frac{1}{2})(\frac{2}{3})(-4) = \frac{4}{3}$Sum $= -\frac{1}{3} - \frac{8}{3} + 2 + \frac{4}{3} = \frac{-1-8+4}{3} + 2 = -\frac{5}{3} + 2 = \frac{1}{3}$.Note: The original expression $ab+bc+ca$ evaluates to $-1$ for these specific variables.

If $a = \frac{x}{y-z}$,$b = \frac{y}{z-x}$,and $c = \frac{z}{x-y}$,where $x, y$,and $z$ are distinct such that $x-y, y-z, z-x \neq 0$,then what is the value of $ab + bc + ca + abc$?

Similar Questions

If $\tan^2 \alpha \tan^2 \beta + \tan^2 \beta \tan^2 \gamma + \tan^2 \gamma \tan^2 \alpha + 2\tan^2 \alpha \tan^2 \beta \tan^2 \gamma = 1$,then the value of $\sin^2 \alpha + \sin^2 \beta + \sin^2 \gamma$ is

If $0 \leq x \leq \frac{\pi}{2}$, then the number of values of $x$ for which $\sin x - \sin 2x + \sin 3x = 0$ is

If $\tan \beta = \cos \theta \tan \alpha ,$ then ${\tan ^2}\frac{\theta }{2} = $

The extreme values of $4 \cos \left(x^2\right) \cos \left(\frac{\pi}{3}+x^2\right) \cos \left(\frac{\pi}{3}-x^2\right)$ over $\mathbb{R}$ are

Observe that,at any instant,the minute and hour hands of a clock make two angles between them whose sum is $360^{\circ}$. At $6:15$,the difference between these two angles is $....^{\circ}$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module