Question : If $x+y+z = 22$ and $xy+yz+zx = 35$, then what is the value of $\small (x-y)^{2}+(y-z)^{2}+(z-x)^{2}$?
Option 1: 793
Option 2: 681
Option 3: 758
Option 4: 715
Latest: SSC CGL preparation tips to crack the exam
Don't Miss: SSC CGL complete guide
New: Unlock 10% OFF on PTE Academic. Use Code: 'C360SPL10'
Correct Answer: 758
Solution : Given: $x+y+z = 22$ and $xy+yz+zx = 35$ We know that $(x+y+z)^2 = x^2+y^2+z^2+2(xy+yz+zx)$ ⇒ $22^2 = x^2+y^2+z^2+2\times 35$ ⇒ $484 = x^2+y^2+z^2+70$ ⇒ $x^2+y^2+z^2 = 484-70 = 414$ So, $(x-y)^2+(y-z)^2+(z-x)^2 = 2[x^2+y^2+z^2-(xy+yz+zx)]$ ⇒ $(x-y)^2+(y-z)^2+(z-x)^2 = 2[414-35]$ $\therefore(x-y)^2+(y-z)^2+(z-x)^2 = 758$ Hence, the correct answer is 758.
Candidates can download this ebook to know all about SSC CGL.
Answer Key | Eligibility | Application | Selection Process | Preparation Tips | Result | Admit Card
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 : $x,y,$ 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 $xy+yz+zx$?
Question : If $xy+yz+zx=1$ , then the value of $\frac{1\:+\:y^2}{(x\:+\:y)(y\:+\:z)}$ is:
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 $x^{2}+y^{2}+z^{2}=14$ and $xy+yz+zx=11$, then the value of $(x+y+z)^{2}$ is:
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile