b^(4)quad " (iii) "(1)/(2a+b+2x)=(1)/(2a)+(1)/(b)+(1)/(2x)

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

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

Expand : (i) (3a-5b)^(2) " " (ii) (a+(1)/(a))^(2) " " (iii) (2x-(1)/(2x))^(2) .

Find the product : (i) (x+3)(x^(2)-3x+9) " " (ii) (7+5b)(49-35b+25b^(2)) (iii) (5a+(1)/(2)) (25a^(2)-(5a)/(2)+(1)/(4)) " " (iv) (a+b-2)[a^(2)+b^(2)+4(a+b)+4] .

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))

Let X=[{:(x_(1)),(x_(2)),(x_(3)):}],A=[{:(1,-1,2),(2,0,1),(3,2,1):}] and B=[{:(3),(1),(4):}] .If AX=B, then X is equal to: a) [(1),(2),(3)] b) [(-1),(2),(3)] c) [(-1),(-2),(3)] d) [(-1),(-2),(-3)]

Prove that (i) (a^(-1))/(a^(-1) + b^(-1)) + (a^(-1))/(a^(-1)-b^(-1)) = (2b^(2))/(b^(2) -a^(2)) (ii) (1)/(1+x^(a-b)) + (1)/(1+x^(b-a)) = 1

If sin^(-1)((2a)/(1+a^2))+sin^(-1)((2b)/(1+b^2))=2tan^(-1)x , then x is equal to [a , b , in (0,1)] (a)(a-b)/(1+a b) (b) b/(1+a b) (c) b/(1+a b) (d) (a+b)/(1-a b)

If sin^(-1)((2a)/(1+a^2))+sin^(-1)((2b)/(1+b^2))=2tan^(-1)x , then x is equal to [a , b , in (0,1)] (a) (a-b)/(1+a b) (b) b/(1+a b) (c) b/(1+a b) (d) (a+b)/(1-a b)

If sin^(-1)((2a)/(1+a^2))+sin^(-1)((2b)/(1+b^2))=2tan^(-1)x , then x is equal to [a , b , in (0,1)] (a) (a-b)/(1+a b) (b) b/(1+a b) (c) b/(1+a b) (d) (a+b)/(1-a b)