WBJEE · Maths · Matrices
If \(\left|\begin{array}{lll}x^k & x^{k+2} & x^{k+3} \\ y^k & y^{k+2} & y^{k+3} \\ z^k & z^{k+2} & z^{k+3}\end{array}\right|=(x-y)(y-z)(z-x)\left(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\right)\), then
- A \(\mathrm{k}=-3\)
- B k=3
- C k=1
- D k=-1
Answer & Solution
Correct Answer
(D) k=-1
Step-by-step Solution
Detailed explanation
\begin{aligned} \text { Hint : } & (x y z)^k\left|\begin{array}{ccc}1 & x^2 & x^3 \\ 1 & y^2 & y^3 \\ 1 & z^2 & z^3\end{array}\right| \\ & =(x y z)^k(x-y)(z-x)-(y-z)(x y+y z+z x) \\ & =(x y z)^{k+1}(x-y)(z-x)-(y-z)\left(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\right) \\ & k+1=0 \\ &…
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