Question : If $x+y+z=0$, then what is the value of $\frac{x^2}{(y z)}+\frac{y^2}{(x z)}+\frac{z^2}{(x y)}$?
Option 1: 1
Option 2: 0
Option 3: 2
Option 4: 3
Latest: SSC CGL 2024 final Result Out | SSC CGL preparation tips to crack the exam
Don't Miss: SSC CGL Tier 1 Scorecard 2024 Released | SSC CGL complete guide
Suggested: Month-wise Current Affairs | Upcoming Government Exams
Correct Answer: 3
Solution : Given: $x+y+z=0$ Cubing both sides, we get, $⇒(x+y+z)^3=0$ $⇒x^3 + y^3 + z^3 + 3(x+y)(y+z)(z+x)=0$ $⇒x^3+y^3+z^3 = -3(x+y)(y+z)(z+x)$ ......(1) From the given equation ($x+y+z=0$), we can get, $x+y=-z,$ $y+z=-x$ and $z+x=-y$ Putting in (1), we get, $x^3+y^3+z^3 = -3(-z)(-x)(-y)=3xyz$ Consider, $\frac{x^2}{(y z)}+\frac{y^2}{(x z)}+\frac{z^2}{(x y)}$ $=\frac{x^2(xz)(xy)+y^2(yz)(xy)+z^2(yz)(xz)}{(yz)(xz)(xy)}$ $=\frac{x^4yz+y^4zx+z^4xy}{x^2y^2z^2}$ Taking $xyz$ as common, we get, $=\frac{xyz(x^3+y^3+z^3)}{x^2y^2z^2}$ $=\frac{x^3+y^3+z^3}{xyz}$ $=\frac{3xyz}{xyz}$ $=3$ Hence, the correct answer is 3.
Candidates can download this ebook to know all about SSC CGL.
Admit Card | Eligibility | Application | Selection Process | Preparation Tips | Result | Answer Key
Question : If $\frac{(x+y)}{z}=2$, then what is the value of $[\frac{y}{(y-z)}+\frac{x}{(x-z)}]?$
Option 1: $0$
Option 2: $1$
Option 3: $2$
Option 4: $–1$
Question : If $x+y+z=0$, then what is the value of $\frac{x^2}{yz}+\frac{y^2}{xz}+\frac{z^2}{xy}$?
Option 2: $\frac{1}{3}$
Option 3: $1$
Option 4: $3$
Question : If $\frac{1}{x+\frac{1}{y+\frac{2}{z+\frac{1}{4}}}}=\frac{29}{79}$, where x, y, and z are natural numbers, then the value of $(2 x+3 y-z)$ is:
Option 1: 0
Option 2: 4
Option 3: 1
Option 4: 2
Question : If $x+y+z=0$, then what is the value of $\frac{x^2}{3z}+\frac{y^3}{3xz}+\frac{z^2}{3x}$?
Option 2: $xz$
Option 3: $y$
Option 4: $3y$
Question : If $x+y+z=0$, then the value of $\frac{x^2}{yz}+\frac{y^2}{zx}+\frac{z^2}{xy}$ is:
Option 1: 3
Option 2: 1
Option 3: 0
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile