If b is the geometric mean of a and c, then show that `a^2 b^2 c^2 [1/a^3 +1/b^3 +1/c^3] =a^3 +b^3 +c^3`.

Fill in the blanks to prove that b is the geometric mean of a and c, if (a-b+c)/(ab+c^2) =1/(b+c)

If a:b=3:1 and b:c=5:1 , then find the value of ((a^3)/(15b^2c))^3

Show that C_1 + C_2 + C_3 +...+ C_6 = 63

Select and write the correct answer from the given alternatives in each of the following:If a!=b!=c!=0 such that |(a^3-1,b^3-1,c^3-1),(a,b,c),(a^2,b^2,c^2)|=0

If sin^4 A/a+cos^4 A/b=1/(a+b) , then the value of sin^8 A/a^3+cos^8 A/b^3 is equal to (A) 1/(a+b)^3 (B) (a^3b^3)/(a+b)^3 (C) (a^2b^2)/(a+b)^2 (D) none of these

Solve the triangle in which a=2 , b=1 and c=sqrt3

Show that : C_1 + C_2 + C_3 + …. + C_7 = 127