If `A,A_1,A_2` and `A_3` are the areas of the inscribed and escribed circles of a triangle, prove that `1/sqrtA=1/sqrt(A_1)+1/sqrt(A_2)+1/sqrt(A_3)`

If a_1,a_2,a_3,………a_n are in A.P, where a_igt0 for all i show that 1/(sqrt(a_1)+sqrt(a_2))+1/(sqrt(a_2)+sqrt(a_3))+……..+1/(sqrt(a_(n-1))+sqrt(a_n))=(n-1)/(sqrt(a_1)+sqrt(a_n))

If a_1,a_2,a_3 and a_4 be any four consecutive coefficients in the expansion of (1+x)^n , prove that a_1/(a_1+a_2)+a_3/(a_3+a_4)= (2a_2)/(a_2+a_3)

Three rectangles A_1, A_2 and A_3 have the same area. Their lengths a_1, a_2 and a_3 respectively are such that a_1

If A1,A2,A3,.......A51 are arithmetic means inserted between the numbers a and b, then find the value of ((b+A51)/(b-A51))-((A1+a)/(A1-a))

If the point A_1, A_2,….,A_8 be the affixes of the roots of the equation z^8-1=0 in the argand plane, then the area of the triangle A_3 A_6 A_7 is equal to

If K_(a_1),K_(a_2) and K_a_3) be the first, second and third dissociation constant of H_(3)PO_(4) and K_(a_1)gtgt K_(2_a) gtgtK_(a_3) whis is/are correct :

If (b_2-b_1)(b_3-b-1)+(a_2-a_1)(a_3-a_1)=0 , then prove that the circumcenter of the triangle having vertices (a_1,b_1),(a_2,b_2) and (a_3,b_3) is ((a_2+a_3)/(2),(b_2+b_3)/(2)) .

If 1, a_1,a_2,a_3 ,…, a_(n-1) are the nth roots of unity then prove that : 1+a_1+a_2+…+a_(n-1) =0.