हल कीजिए:
`2(x^(2)+1/x^(2))-3(x+1/x)-1=0`

(x^3+1/x^3)+(x^2+1/x^2)-6(x+1/x)-7=0

I : If (x^(2)+x+1)/(x^(2)+2x+1)=A+B/(x+1)+C/(x+1)^(2) " then "A+B+C=0 . II : If (x^(2)+2x+3)/x^(3)=A/x+B/x(2)+C/x^(3) " then "A+B-C=0 .

If xgt0 then (x-1)/(x+1)+(1)/(2)(x^(2)-1)/((x+1)^(2))+(1)/(3)(x^(3)-1)/((x+1)^(3))+....=

If xgt0 then (x-1)/(x+1)+(1)/(2)(x^(2)-1)/((x+1)^(2))+(1)/(3)(x^(3)-1)/((x+1)^(3))+....=

If |{:(x^(2) +x , 3x - 1 , -x + 3),(2x +1 , 2 + x^(2) , x^(3) - 3),(x - 3, x^(2) + 4, 3x):}| = a_(0) + a_(1) x + a_(2) x^(2) + .... + x_(7) x^(7), then the value of a_(0) is

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

(1)/(x)-(1)/(x-2)=3,x!=0,2

lim_(x rarr0)(sqrt(1+x^(2))-sqrt(1-x^(2)))/(3^(x)-1)=