[" Q.3If "a:b=c:d" than prove by "K" method "],[" That "quad (a^(2)+c^(2))/(b^(2)+d^(2))=(ac)/(bd)]

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

If a : b = c : d , then prove that the - proportional of (a^(2) + c^(2)) " and " (b^(2) + d^(2)) " is " (ab + cd) .

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 prove that : (a^(2) + ac + c^(2)) : (a^(2) - ac + c^(2)) = (b^(2) + bd + d^(2)) : (b^(2) - bd + d^(2))

(i) If a , b , c are in continued proportion, show that : (a^(2) + b^(2))/(b(a+c)) = (b(a + c))/(b^(2) + c^(2)) . (ii) If a , b , c are in continued proportion and a(b - c) = 2b , prove that : a - c = (2(a + b))/(a) . (iii) If (a)/(b) = (c)/(d) show that : (a^(3)c + ac^(3))/(b^(3)d +bd^(3)) = ((a + c)^(4))/((b + d)^(4)) .

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 GP, prove that (b-c)^(2)+(c-a)^(2)+(d-b)^(2)=(a-d)^(2) .

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

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

If a sec theta-c tan theta=d and b sec theta+d tan theta=c ,then prove that (c^(2)+d^(2))^(2)-(ac-bd)^(2)=(ad+bc)^(2)