Question

If $\left| \begin{matrix} x^{n} & x^{n + 2} & x^{n + 3} \\ y^{n} & y^{n + 2} & y^{n + 3} \\ z^{n} & z^{n + 2} & z^{n + 3} \end{matrix} \right|$ = (x – y)(y – z)(z–x) $\left( \frac{1}{x} + \frac{1}{y} + \frac{1}{z} \right)$

then value of n is –

• A. – 1
• B. – 2
• C. 1
• D. 2

Answer 1

Answer: (A)

– 1

Answer 2

Degree of L.H.S = n + (n + 2) + (n + 3) = 3 n + 5 ……. (1)

Degree of R.H.S = 1 + 1 + 1 + (–1) = 2 ……. (2)

from (1) & (2)

3 n + 5 = 2 Ž n = – 1