" 34."x^(2)+(1)/(x^(2))-2-3x+(3)/(x)

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))

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)

im_(-)>1[(x-2)/(x^(2)-x)-(1)/(x^(3)-3x^(2)+2x)]

(x^(2)-x)-(1)/(2)(x-3+3x^(2))

Find (x)/(1.2)+(x^(2))/(2.3)+(x^(3))/(3.4)+....=

Show that : x^(2)+ (1)/(x^(2)) = 34 , if x =3 + 2sqrt(2)

lim_(xrarr1) [(x-2)/(x^(2)-x)-(1)/(x^(3)-3x^(2)+2x)]

lim_(xrarr1) [(x-2)/(x^(2)-x)-(1)/(x^(3)-3x^(2)+2x)]

Let tan^(-1)y=tan^(-1)x+tan^(-1)((2x)/(1-x^(2))) where |x|<(1)/(sqrt(3))* Then a value of y is : (1)(3x-x^(3))/(1-3x^(2))(2)(3x+x^(3))/(1-3x^(2))(3)(3x-x^(3))/(1+3x^(2))(4)(3x+x^(3))/(1+3x^(2))