The most simplified form of `(a^2-c^2+2b(a-c))/(2abc+ab(a+b)+ac(a+c)+bc(b+c))` is

If the product abc =1, then the value of the determinant |{:( -a ^(2), ab, ac),( ba, -b ^(2), bc),(ac, bc,-c ^(2)):}| is

If a,b, and c are in H.P.then th value of ((ac+ab-bc)(ab+bc-ac))/((abc)^(2)) is ((a+c)(3a-c))/(4a^(2)c^(2)) b.(2)/(bc)-(1)/(b^(2)) c.(2)/(bc)-(1)/(a^(2)) d.((a-c)(3a+c))/(4a^(2)c^(2))

Using properties of determinants, prove the following abs{:(a^2, bc, ac +c^2 ),(a^(2) + ab, b^(2),ac ),(ab, b^(2) + bc,c^(2) ):}=4a^(2) b^(2) c^(2) .

If a^(2)+b^(2)+c^(2)-ab-bc-ca=0, then a+b=c( b) b+c=ac+a=b(d)a=b=c

(a+b+c)(a^(2)+b^(2)+c^(2)-ab-bc-ac)

If a,b,c in R^(+), then (bc)/(b+c)+(ac)/(a+c)+(ab)/(a+b) is always (a) (a) =(1)/(3)sqrt(abc)(c) =(1)/(2)sqrt(abc)

(b + c) ^ (2), ab, caab, (a + c) ^ (2), bcac, bc, (a + b) ^ (2)] | = 2abc (a + b + c) ^ ( 3)

Using properties of determinants, show the following: |[(b+c)^2,ab, ca],[ab,(a+c)^2,bc ],[ac ,bc,(a+b)^2]|=2abc(a+b+c)^3

If (a^(2)-bc)/(a^(2) +bc) + (b^(2)-ac)/(b^(2) + ac) + (c^(2)-ab)/(c^(2)+ab)= 1 then find (a^(2))/(a^(2) + bc) + (b^(2))/(b^(2) + ac) + (c^(2))/(c^(2) +ab)= ?