ab+bc+a^(2)+ac

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, b and c are distinct positive real numbers such that Delta_(1) = |(a,b,c),(b,c,a),(c,a,b)| and Delta_(2) = |(bc - a^2, ac -b^2, ab - c^2),(ac - b^2, ab - c^2, bc -a^2),(ab -c^2, bc - a^2, ac - b^2)| , then

If a, b, c are in HP show that ab + bc = 2ac.

Show that |(0,a,c),(a,0,b),(c,b,0)|^(2)=|(2ac,ab,bc),(ab,-a^(2),-ac+b^(2)),(bc,-ac+b^(2),-c^(2))|

If |{:(bc-a^(2),ac-b^(2),ab-c^(2)),(ac-b^(2),ab-c^(2),bc-a^(2)),(ab-c^(2),bc-a^(2),ac-b^(2)):}|=k(a^(3)+b^(3)+c^(3)-3abc)^(l) then the value of (k, l) is

If ∣ -a a^2 ab ac ab -b^2 bc ac bc -c^2 | = ka^2b^2c^2 , then k is equal to

If in the expansion of (1+x)^(n),a,b,c are three consecutive coeficients,then n=(ac+ab+bc)/(b^(2)+ac) b.(2ac+ab+bc)/(b^(2)-ac) c.(ab+ac)/(b^(2)-ac) d.none of these

Subtract : 2 ab + 5 bc - 7 ac from 5 ab - 2 bc - 2 ac + 10 abc

|(-a^(2),ab,ac),(ab,-b^(2),bc),(ac,bc,-c^(2))|=

What is |{:(-a^(2),ab,ac),(ab,-b^(2),bc),(ac,bc,-c^(2)):}| equal to ?