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)`

(x+1) sqrt(2x^(2)+3)

If a_(1), a_(2), a_(3),……,a_(n) are in AP, where a_(i) gt 0 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, ,a_n are in A.P., where a_i >0 for all i , show that 1/(sqrt(a_1)+sqrt(a_2))+1/(sqrt(a_1)+sqrt(a_3))++1/(sqrt(a_(n-1))+sqrt(a_n))=(n-1)/(sqrt(a_1)+sqrt(a_n))dot

Which term of the sequence sqrt2, (1)/(sqrt2), (1)/(2 sqrt2) ……is (1)/(512 sqrt2) ?

The incentre of triangle with vertices (1, sqrt(3)), (0,0) and (2, 0) is

Prove that the following are irrationals (1) (1)/sqrt(2) (2) 7sqrt(5) (3)6+sqrt(2)

x=sqrt(1+2sqrt(1+3sqrt(1+4sqrt(1+... , then x is

If three unequel numbers are in HP and their squares are in AP, show that they are in the ratio 1+sqrt(3):-2:1-sqrt(3) " or " 1-sqrt(3):-2:1+sqrt(3) .

Find 6^(th) term of a G.P. sqrt3, (1)/(sqrt3), (1)/(3 sqrt3) ……

Prove the following by using the principle of mathematical induction for all n in N sqrtn lt= (1)/(sqrt1) + (1)/(sqrt2) + ……+ (1)/(sqrtn)