If x+y+z=0, then what is the value of frac{x^ | vedclass

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

Question

(A) Given that $x+y+z=0.$We need to find the value of the expression $E = \frac{x^{2}}{3yz} + \frac{y^{2}}{3xz} + \frac{z^{2}}{3xy}.$Taking the least

Vedclass · Accepted Answer

$0$

Vedclass · Answer

(A) Given that $x+y+z=0.$We need to find the value of the expression $E = \frac{x^{2}}{3yz} + \frac{y^{2}}{3xz} + \frac{z^{2}}{3xy}.$Taking the least common multiple $(LCM)$ of the denominators $3yz, 3xz,$ and $3xy,$ which is $3xyz,$$E = \frac{x^{2}(x) + y^{2}(y) + z^{2}(z)}{3xyz} = \frac{x^{3} + y^{3} + z^{3}}{3xyz}.$We know the algebraic identity that if $x+y+z=0,$ then $x^{3} + y^{3} + z^{3} = 3xyz.$Substituting this into our expression:$E = \frac{3xyz}{3xyz} = 1.$Note: Based on the provided options and the structure of the expression,the result is $1$. If the expression was $\frac{x^3}{3yz} + \dots$ or similar,the result would vary. Given the standard form of this identity,the value is $1$.

If $x+y+z=0,$ then what is the value of $\frac{x^{2}}{3yz} + \frac{y^{2}}{3xz} + \frac{z^{2}}{3xy}?$

Similar Questions

Let $f(x) = a_{0}x^{n} + a_{1}x^{n-1} + a_{2}x^{n-2} + \ldots + a_{n-1}x + a_{n}$,where $a_{0}, a_{1}, a_{2}, \ldots, a_{n}$ are constants. If $f(x)$ is divided by $ax - b$,then the remainder is:

If $2x + \frac{1}{2x} = 2$,then what is the value of $\sqrt{2(\frac{1}{x})^4 + (\frac{1}{x})^5}$?

If $p=99,$ then the value of $p(p^{2}+3p+3)$ is

If $x+\frac{1}{x}=2,$ then $x^{3}+\frac{1}{x^{3}}$ is equal to

Divide the polynomial $4y^{3}-3y^{2}+2y-4$ by $y+2$ and find the quotient and remainder.

Vedclass Test Series

Exam Paper Generator

Online Exam Module