4cd(c^(2)+d^(2))," if "c+d=11,c-d=

Find the value of 4cd(c^(2)+d^(2))quad if c+d=11,c-d=1

If (a)/(b)=(c)/(d) then (a+b)/(a-b)=(c+d)/(c-d),ab=cd ,(a^(2)+b^(2))/(a^(2)-b^(2))=(c^(2)+d^(2))/(c^(2)-d^(2)), ad-dc=0

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^(2) + c^(2)) , (ab + cd) and (b^(2) + d^(2)) are in continued proportion, prove that a , b , c and d are in proportion.

If a/b = b/c = c/d , then prove that (a^(2) + b^(2) + c^(2))(b^(2) + c^(2)+d^(2)) = (ab + bc cd)^(2)

If a,b,c,d and p are distinct real numbers such that (1987,2M)(a^(2)+b^(2)+c^(2))p^(2)-2(ab+bc+cd)P+(b^(2)+c^(2)+d^(2))>=0, then a,b,c,d are in AP(b) are in GP are in HP(d) satisfy ab=cd

Given four quantities a , b , c and d are in proportion. Show that : (a - c)b^(2) : (b - d)cd = (a^(2) - b^(2) - ab) : (c^(2) - d^(2) - cd)

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

If a, b, c ,d be in G.P. , show that (i) (b -c)^(2) + (c - a)^(2) +(d -b)^(2) = (a - d)^(2) (ii) a^(2) + b^(2) + c^(2) , ab + bc + cd , b^(2) + c^(2) + d^(2) are in G.P.