Show that `(a-b)(a+b)+(b-c)(b+c)+(c-a)(c+a)`=0

Show that If a(b-c) x^2 + b(c-a) xy + c(a-b) y^2 = 0 is a perfect square, then the quantities a, b, c are in harmonic progresiion

If a,b,c are in AP, than show that a^(2)(b+c)+b^(2)(c+a)+c^(2)(a+b)=(2)/(9)(a+b+c)^(3) .

If a,b,c are in HP, then prove that (a+b)/(2a-b)+(c+b)/(2c-b)gt4 .

Using determinants show that points A(a, b + c), B(b, c + a) and C(c, a + b) are collinear.

if one of the root of the equation a(b-c)x^(2)+b(c-a)x+c(a-b)=0 is 1,the other root is

If one of the roots of the equation a(b-c)x^(2)+b(c-a)x+c(a-b)=0 is 1, the other root is

Prove that {:[(1,ab,a+b),(1,bc,b+c),(1,ca,c+a):}]=(a-b)(b-c)(c-a)

Using determinants show that points A (a, b+ c) , B (b,c+ a) and C ( c, a+ b) are collinear.

If (a+bx)/(a-bx)=(b-cx)/(b-cx)=(c+dx)/(c-dx)( x ne 0) then show that a, b, c and d are in G.P.