`((x^2+1)(x^2+2))/((x^2+3)(x^2+4))`

If x^(2)+3x+1=0 then find x^(3)+(1)/(x^(3)),x^(4)+(1)/(x^(4)),x^(2)-(1)/(x^(2)),x^(2)+(1)/(x^(2))

(x+(1)/(x))^(2)-(x-(1)/(x))^(2)=? 1) x^(2)+(1)/(x^(2)) 2) 4 3) 2x^(2)+(1)/(2x^(2)) 4) 2x^(2)+4+(1)/(2x^(2))

Find the sum to n terms of the following series: (x+(1)/(x))^(2)+(x^(2)+(1)/(x^(2)))^(2)+(x^(3)+(1)/(x^(3)))^(2)+(x^(4)+(1)/(x^(4)))^(2)+

Find the sum to n terms of the following series: (x+(1)/(x))^(2)+(x^(2)+(1)/(x^(2)))^(2)+(x^(3)+(1)/(x^(3)))^(2)+(x^(4)+(1)/(x^(4)))^(2)+...

If f(x) = int((1+x)(1-x+x^(2))(1+x+x^(2))+x^(2))/(1+2x+3x^(2)+4x^(3)+3x^(4)+2x^(5)+x^(6)) dx then find the value of [F(99)-F(3)].[Note :[k] denotes greatest integer less than or equal to k.]

Check whether the following are quadratic equations : (1) (x-1)^(2)=2(x-3) (2) x^(2)-2x=(-2)(3-x) (3) (x-2)(x+1)=(x-1)(x+3) (4) (x-3)(2x+1)=x(x+5) (5) (2x-1)(x-3)=(x+5)(x-1) (6) x^(2)+3x+1=(x-2)^(2) (7) (x+2)^(3)=2x(x^(2)-1) (8) x^(3)-4x^(2)-x+1=(x-2)^(3)