If `|[x^(n-1), x^(n+1), x^(n+2)] ,[y^(n-1), y^(n+1), y^(n+2)], [z^(n-1), z^(n+1), z^(n+2)]|= (x-y)(y-z)(z-x)(x^(-1)+y^(-1)+z^(-1))` then `n=`

If |(x^(n),x^(n+2),x^(n+3)),(y^(n),y^(n+2),y^(n+3)),(z^(n),z^(n+2),z^(n+3))| = (x -y) (y -z) (z -x) ((1)/(x) + (1)/(y) + (1)/(z)) , then n equals

Let n be an integer and x,y,z lt1 . Suppose Delta=|(x^(n+1),x^(n+2),x^(n+3)),(y^(n+1),y^(n+2),y^(n+3)),(z^(n+1),z^(n+2),z^(n+3))| If Delta=(x-y)(y-z)(z-x)x^(2)y^(2)z^(2) then n is equal to

If |x^n x^(n+2)x^(n+3)y^n y^(n+2)y^(n+3)z^n z^(n+2)z^(n+3)|=(x-y)(y-z)(z-x)(1/x+1/y+1/z), then n equals 1 b. -1 c. 2 d. -2

Simplify : (x^(2^(n-1)) + y^(2^(n-1)))(x^(2^(n-1)) - y^(2^(n-1)))

If |x^n x^(n+2)x^(n+4)y^n y^(n+2)y^(n+4)z^n z^(n+2)z^(n+4)|=(1/(y^2)-1/(x^2))(1/(z^2)-1/(y^2))(1/(x^2)-1/(z^2)) then n is __________.

If x + y = 1, show that D ^ (n) (x ^ (n) y ^ (n)) = n! [Y ^ (n) - (nC_ (1)) ^ (2) y ^ (n -1) x + (nC_ (2)) ^ (2) y ^ (n-2) x ^ (2) + ...... + (- 1) ^ (n) x ^ (n)]

If x=a^(m+n),y=a^(n+l) and z=a^(l+m), prove that x^(m)y^(n)z^(l)=x^(n)y^(l)z^(m)

If x=a^(m+n),y=a^(n+1) and z=a^(l+m) prove that x^(m)+y^(n)z^(l)=x^(n)y^(l)z^(m)