Question : If $x^{2}+y^{2}+z^{2}=xy+yz+zx$, then the value of $\frac{3x^{4}+7y^{4}+5z^{4}}{5x^{2}y^{2}+7y^{2}z^{2}+3z^{2}x^{2}}$ is:
Option 1: 2
Option 2: 1
Option 3: 0
Option 4: –1
Latest: SSC CGL Tier 1 Result 2024 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: 1
Solution : Given: $x^{2}+y^{2}+z^{2}=xy+yz+zx$ ⇒ $x^{2}+y^{2}+z^{2}-xy-yz-zx=0$ ⇒ $\frac{1}{2}[(x-y)^{2}+(y-z)^{2}+(z-x)^{2}]=0$ So, $(x-y)=0$, $(y-z)=0$, $(z-x)=0$ So, $x=y=z$ Putting this value in the given condition, we have: $\frac{3x^{4}+7y^{4}+5z^{4}}{5x^{2}y^{2}+7y^{2}z^{2}+3z^{2}x^{2}}=\frac{15x^{4}}{15x^{4}}=1$ Hence, the correct answer is 1.
Candidates can download this ebook to know all about SSC CGL.
Admit Card | Eligibility | Application | Selection Process | Preparation Tips | Result | Answer Key
Question : If $x+y+z=0$, then the value of $\frac{x^2}{yz}+\frac{y^2}{zx}+\frac{z^2}{xy}$ is:
Question : If $\frac{x^2}{yz}+\frac{y^2}{zx}+\frac{z^2}{xy}=3$, then what is the value of $(x+y+z)^3$?
Question : If $x+y+z=0$, then what is the value of $\frac{x^2}{yz}+\frac{y^2}{xz}+\frac{z^2}{xy}$?
Question : If $x+y+z=0$, then what is the value of $\frac{x^2}{3z}+\frac{y^3}{3xz}+\frac{z^2}{3x}$?
Question : $x,y,$ and $z$ are real numbers. If $x^3+y^3+z^3 = 13, x+y+z = 1$ and $xyz=1$, then what is the value of $xy+yz+zx$?
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile