[" 8.Prove that: "],[[a+b,c+d],[-c+d,a-b]|=a^(2)-b^(2)+c^(2)-d^(2)]

If a, b, c, d are in G.P., prove that a^(2) - b^(2), b^(2)-c^(2), c^(2)-d^(2) are also in G.P.

a,b,c,d are in G.P. Prove that a^(2)-b^(2),b^(2)-c^(2), c^(2)-d^(2) are also in G.P.

If a, b, c, d are in GP, prove that (a^(2)-b^(2)), (b^(2)-c^(2)), (c^(2)-d^(2)) are in GP.

Prove that |(a,b),(c,d)|^(2)=|(a^(2)+c^(2),ab+cd),(ab+cd,b^(2)+d^(2))|

If a,b,c,d,e are in continued proportion,then prove that (ab+bc+cd+de)^(2)=(a^(2)+b^(2)+c^(2)+d^(2))(b^(2)+c^(2)+d^(2)+e^(2))

If a, b, c, d are in G.P., then prove that: (b-c)^(2)+(c-a)^(2)+(d-b)^(2)=(a-d)^(2)

If a,b,c,d are in G.P.prove that: (a^(2)+b^(2)),(b^(2)+c^(2)),(c^(2)+d^(2)) are in G.P.(a^(2)-b^(2)),(b^(2)-c^(2)),(c^(2)-d^(2)) are in G.P.(1)/(a^(2)+b^(2)),(1)/(b^(2)+c^(2)),(1)/(c^(2)+d^(2)) are in G.P.(a^(2)+b^(2)+c^(2)),(ab+bc+cd),(b^(2)+c^(2)+d^(2))

If a ,b,c , d are in G.P. prove that (a-d)^(2) = (b -c)^(2)+(c-a)^(2) + (d-b)^(2)

If a, b, c, d are in continued proportion, then prove that (b -c)^(2) + (c -a)^(2) + (b-d)^(2) = (a -d)^(2)

If a : b = c : d , then prove that (a + c) : (b + d) = sqrt(a^(2) - c^(2)) : sqrt(b^(2) - d^(2))