AP EAMCET · Maths · Functions
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 \(6\)
- B \(3\)
- C \(9\)
- D \(12\)
Answer & Solution
Correct Answer
(B) \(3\)
Step-by-step Solution
Detailed explanation
\(x+y+z=1\) \(\begin{aligned} & x^2+y^2+z^2=1 \\ & x^3+y^3+z^3=1\end{aligned}\) 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 \((1,0,0)\)
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