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 $xy+yz+zx$?
Option 1: –1
Option 2: 1
Option 3: 3
Option 4: –3
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: –3
Solution : Given: $x^{3}+y^{3}+z^{3}=13$, $ x+y+z=1$, $xyz=1$ We know, $x^{3}+y^{3}+z^{3}-3xyz= (x^{2}+y^{2}+z^{2}-xy-yz-zx)$ $⇒x^{3}+y^{3}+z^{3}-3xyz= (x+y+z)((x+y+z)^{2}-3(xy+yz+zx))$ Substituting values of $x^{3}+y^{3}+z^{3}$, $ x+y+z$ and $xyz$, $⇒13-3(1)=(1)((1^{2}-3(xy+yz+zx))$ $⇒xy+yz+zx=\frac{10-1}{-3}$ $\therefore xy+yz+zx=-3$ 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 $(x+y+z)=12$, $xy+yz+zx=44$, and $xyz=48$, then what is the value of $x^{3}+y^{3}+z^{3}$?
Question : If $x+y+z = 22$ and $xy+yz+zx = 35$, then what is the value of $\small (x-y)^{2}+(y-z)^{2}+(z-x)^{2}$?
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 $xy+yz+zx=1$ , then the value of $\frac{1\:+\:y^2}{(x\:+\:y)(y\:+\:z)}$ 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