`(sqrta+sqrtb)(sqrta-sqrtb)`

If 4/(2+sqrt3+sqrt7)=sqrta+sqrtb-sqrtc ,then which of the following can be true -

If sqrt(9+sqrt48-sqrt32-sqrt24)=sqrta-sqrtb+2 ,where a,b inN , then find the value of a + b.

If a,b,c are in A.P., then prove that the following are also in A.P (i) a^(2)(b+c),b^(2)(c+a),c^(2)(a+b) ltbr gt(ii) 1/(sqrtb+sqrtc),1/(sqrtc+sqrta),1/(sqrta+sqrtb) (iii) a(1/b+1/c),b(1/c+1/a),c(1/a+1/b)

If one root of the quadratic equation px^2 +qx + r = 0 (p != 0) is a surd sqrta/(sqrta+sqrt(a-b), where p, q, r; a, b are all rationals then the other root is -

Let sqrta+sqrtd=sqrtc+sqrtb and ad=bc , where a, b, c, in R^(+) . If the family of lines (a^(2)x+b^(2)y+c^(2))+d^(2)x=0 passes through a fixed point (x_(0), y_(0)) , then the value of (x_(0)+y_(0)) is

If sum of first n terms of an AP (having positive terms) is given by S_n=(1+2T_n)(1-T_n) , where T_n is the nth term of series , and T_2^2=(sqrta-sqrtb)/4 (a,b in N) . Then (a+b) is ____

If a 0, then sqrta. sqrtb is equal to :

If the value of the definite integral int ^(-1) ^(1) cos ^(-1) ((1)/(sqrt(1-x ^(2)))) . (cot ^(-1)""(x )/(sqrt (1-(x ^(2))^(|x|))))dx = (pi^(2)(sqrta-sqrtb))/(sqrtc) where a,b,c in N in their lowest from, then find the value of (a+b+c).

The term independent of a in the expansion of (1+sqrta+ 1/(sqrta-1))^-30 is (a) 30C_20 (b) 0 (c) 30C_10 (d) non of these

The area of the region bounded by the curve sqrtx+sqrty=sqrta(x,ygt0) and the coondinate axes is