The value of `|(x,x+2),(x+1,x+3)|` is _____

If x ^(2) - 3 sqrt2 x +1 = 0, then the value of x ^(3) + (1)/(x ^(3)) is :

If (x+(1)/(x))=3, then the value of (x^(2)+(1)/(x^(2))) is:

If x^2 - 3x + 1 = 0 , then the value of (x^6 + x^4 + x^2 + 1)/(x^3) will be

If x_(1),x_(2),x_(3),.......x_(n) are the roots of x^(n)+ax+b=0, then the value of (x_(1)-x_(2))(x_(1)-x_(3))(x_(1)-x_(4))......(x_(1)x_(n)) is equal to