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 are in G.P.then (a^(2)-b^(2)),(b^(2)-c^(2)),(c^(2)-d^(2)) are in

If a:b=c:d then value of (a^(2)+b^(2))/(c^(2)+d^(2)) is

If (2a+3b)(2c-3d)=(2a-3b)(2c+3d) then (a)/(b)=(c)/(d)( b) (a)/(d)=(c)/(b)( c) (a)/(b)=(d)/(c)(d)(b)/(a)=(c)/(d)

When two ratios are equal, then the four quantities compositing them are said to be proportiona. If a/b=c/d, then it is written a:b=c:dor a:b::c:d. Also if a/b=c/d=lamdaimpliesa=blamdaand c=dlamdaimpliesa/b=c/d =(a+-c)/(b+-d)=(""^(n)sqrt((a)^(n)+-(c)^(n)))/(""^(n)sqrt((b)^(n)+-(d)^(n)))=lamda(lamdagt0) important property of proportion : 1. If a:b=c:d,then (a+b)/(b)=(c+d)/(d)("Componendo")i.e.(a)/(b)=(c)/(d)implies(a)/(b)+1=(c)/(d)+1 2. If a:b=c"d, then (a-b)/(b)=(c-d)/(d)("Dividenod")i.e.(a)/(b)=(c)/(d)implies(a)/(b)-1=(c)/(d)-1 3. If a:b:=c:d, then (a+b)/(a-b)=(c+d)/(c-d)("Componendo and dividendo") If (x^(3)+x^(2)+x+1)/(x^(3)-x^(2)-x-1)=(x^(2)+x1)/(x^(2)-1+1) then the number of real value of x satisfying are

If a, b, c and d are in proportion, then show that (a^(3)+3ab^(2))/(3a^(2)b+b^(3))=(c^(3)+3cd^(2))/(3c^(2)d+d^(3))

If a,b,c,d are in G.P.show that: (ab+bc+cd)^(2)=(a^(2)+b^(2)+c^(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 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 and d are in G.P.show that (a^(2)+b^(2)+c^(2))(b^(2)+c^(2)+d^(2))=(ab+bc+cd)^(2)

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