If x^{2}+y^{2}+z^{2}+2=2(y-x),then the value | vedclass

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

Question

(A) Given equation: $x^{2}+y^{2}+z^{2}+2=2(y-x)$Rearranging the terms: $x^{2}+2x+y^{2}-2y+z^{2}+2=0$Completing the squares: $(x^{2}+2x+1)+(y^{2}-2y+1)

Vedclass · Accepted Answer

$0$

Vedclass · Answer

(A) Given equation: $x^{2}+y^{2}+z^{2}+2=2(y-x)$Rearranging the terms: $x^{2}+2x+y^{2}-2y+z^{2}+2=0$Completing the squares: $(x^{2}+2x+1)+(y^{2}-2y+1)+z^{2}=0$This simplifies to: $(x+1)^{2}+(y-1)^{2}+z^{2}=0$Since the sum of squares is zero,each term must be zero:$x+1=0 \Rightarrow x=-1$$y-1=0 \Rightarrow y=1$$z=0$Therefore,$x^{3}+y^{3}+z^{3} = (-1)^{3} + (1)^{3} + (0)^{3} = -1 + 1 + 0 = 0$.

If $x^{2}+y^{2}+z^{2}+2=2(y-x)$,then the value of $x^{3}+y^{3}+z^{3}$ is equal to

Similar Questions

If $2x + \frac{2}{x} = 1$,then the value of $x^{3} + \frac{1}{x^{3}}$ is

$A$ pineapple costs $Rs. 7$ each. $A$ watermelon costs $Rs. 5$ each. $X$ spends $Rs. 38$ on these fruits. The number of watermelons purchased is

Evaluate $\frac{8-[5-(-3+2)]+2}{|5-3|-|5-8|+3}$

The value of $\frac{1}{1 \cdot 2 \cdot 3} + \frac{1}{2 \cdot 3 \cdot 4} + \frac{1}{3 \cdot 4 \cdot 5} + \frac{1}{4 \cdot 5 \cdot 6}$ is:

What is the difference between the biggest and the smallest fraction among $\frac{2}{3}, \frac{3}{4}, \frac{4}{5}$ and $\frac{5}{6}$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module