गुणनखण्ड कीजिए : `x^(2)-((a)/(b)+(b)/(a))x+1`

सिद्ध कीजिए कि 2tan^(-1)sqrt((b)/(a))=cos^(-1)((a-b)/(a+b))

Show : ( x^(a^2)/ x^( b^2 ) )^ (1/( a+b)) times ( x^(b^2)/ x^( c^2 )) ^ ( 1/( b+c )) times ( x^(c^2)/ x^( a^2 ) )^ (1/( c+a)) = 1

If the polynomial f(x) = |{:((1+x)^(a), (2+x)^(b),1),(1, (1 + x)^(a), (2 + x)^(b)),((2+x)^(b) , 1, (1+x)^(a)) :}| then the constant term of f(x) is

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

If (x^(2))/((x-a)(x-b))=1+(a^(2))/((a-b)(x-a))+(B)/((x-b)) , then B is _________.

Show that : (x^(a(b-c)))/(x^(b(a-c)))*(x^(b))/(x^(a)))^(c)=1((x^(a+b))^(2)(x^(b+c))(x^(c+a))^(2))/((x^(a)x^(b)x^(c))^(4))=1

Prove that. (i) sqrt(x^(-1) y) .sqrt(y^(-1) z) . Sqrt(z^(-1) x) = 1 (ii) ((1)/(x^(a-b)))^((1)/(a-c)).((1)/(x^(b-c))).((1)/(x^(c-b)))^((1)/(c-b))= 1 (iii) (x^(a(b-c)))/(x^(b(a-c))) div ((x^(b))/(x^(a))) (iv) ((x^(a+b))^(2)(x^(b+c))^(2)(x^(c+a))^(2))/((x^(a)x^(b)x^(c))^(4))

Solve: (a+x-2b)/(2a-b)-(a-2b)/x=1 .