Q54 / 160 · AP EAMCET 2022 (05 Jul Shift 2) · Mathematics

The number of solutions of the equations $x+y+z=1 ; x^2+y^2+z^2=1 ; x^3+y^3+z^3=1$ is

  • A
    $6$
  • Correct answer
    B
    $3$
  • C
    $9$
  • D
    $12$

Solution

$x+y+z=1$ $\begin{aligned} & x^2+y^2+z^2=1 \\ & x^3+y^3+z^3=1\end{aligned}$ It is evident from all 3 that equation satisfies only if 2 of them are zero and third is 1. There are 3 solution sets of $(x, y, z)$ $(0,0,1),(0,1,0)$ and $(1,0,0)$

Hence, the correct answer is option: 'B'.

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