If `x ne 0 and x + (1)/(x) = 2`, then show that: `x^(2)+ (1)/(x^(2))= x^(3) + (1)/(x^(3)) = x^(4) + (1)/(x^(4))`

If xx=sqrt(3)+sqrt(2), then find xx+1/x,x^(2)+(1)/(x^(2)),x^(3)+(1)/(x^(3)),x^(4)+(1)/(x^(4))

Let f(x+(1)/(x))=x^(2)+(1)/(x^(2)),(x ne 0) then f(x) equals

If x+1/x=3, calculate x^2+1/(x^2),\ x^3+1/(x^3) and x^4+1/(x^4)

If a ne 0 and a ne 1, show that |{:(x+1,x,x),(x,x+a,x),(x,x,x+a^(2)):}|=a^(3)[1+x((a^(3)-1))/(a^(2)(a-1))].

If a ne 0 and a ne 1, show that |{:(x+1,x,x),(x,x+a,x),(x,x,x+a^(2)):}|=a^(3)[1+x((a^(3)-1))/(a^(2)(a-1))].

If x - (1)/(x) = y , x ne 0 , find the value of (x- (1)/ (x) - 2y ) ^(3)

If the hyperbola xy=c^(2) intersects the circle x^(2)+y^(2)=a^(2)" is four points "P(x_(1),y_(1)), Q(x_(2),y_(2)), R(x_(3),y_(3)) and S(x_(4),y_(4)) then show that (i) x_(1)+x_(2)+x_(3)+x_(4)=0 (ii) y_(1)+y_(2)+y_(3)+y_(4)=0 (iii) x_(1)x_(2)x_(3)x_(4)=c^(4) (iv) y_(1)y_(2)y_(3)y_(4)=c^(4)

The solution set of (x+(1)/(x) ) ^2 -3/2 (x-(1)/(x)) =4 when x ne 0 is

If x^4+1/(x^4)=194 , find x^3+1/(x^3),x^2+1/(x^2) and x+1/x

If x^4+1/(x^4)=194 , find x^3+1/(x^3),x^2+1/(x^2) and x+1/x