If a,b,c, are positive then show that `(a)/(b+c) + (b)/(c+a)+ (c )/(a+b) gt= (3)/(2)` .

If (b-c)^(2) , (c-a)^(2), (a-b)^(2) are in A.P. then prove that (1)/(b-c) , (1)/(c-a), (1)/(a-b) are also in A.P.

If (a)/(b+c),(b)/(c+a),(c)/(a+b) are in AP, then

If (b + c) (y + z) - ax = b - c, (c + a) (z + x) - by = c - a and (a + b) (x + y) - cz = a - b , where a + b + c ne 0, then x is equal to a) (c + b)/(a + b + c) b) (c - b)/(a + b + c) c) (a - b)/(a + b + c) d) (a + b)/(a + b + c)

The equation a cos theta + b sin theta = c has a solution when a,b and c are real numbers such that : a) a lt b lt c b) a = b=c c) c ^(2) lea ^(2) + b ^(2) d) c ^(2) le a ^(2) -b ^(2)

Suppose a, b, c are in A.P. Prove that (a+2b-c)(2b+c-a)(c+a-b)=4abc

If a, b, c are positive and unequal show that value of the determinant Delta=|[a, b, c],[ b, c, a],[ c, a, b]| is negative.

If a, b, c and d are in G . P , show that (a^2+b^2+c^2)(b^2+c^2+d^2)=(ab+b c+cd)^2 .

If a, b and c are distinct reals and the determinant |{:(a ^(3) +1, a ^(2) , a ),( b ^(3) +1, b ^(2) , b ),( c ^(3) +1, c ^(2), c):}|= 0, then the product abc is