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When two ratios are equal, then the four...

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

A

0

B

1

C

2

D

3

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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 ""(a+3d)/(a+9d)=(a+d)/(a+5d)=k, then k is equal to (a,d gt0)

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 a/b=c/d=e/fand(2a^(4)b^(2)+3a^(2)c^(2)-5e^(4)f)/(2b^(6)+3b^(2)d^(2)-5f^(5))=((a)/(b))^(n) then teh value of n is :

If a-b:b-c:c-d=1:2:3 then (a+d):c=

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)

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 ( ( a +c )/( b + d ) ) is equal to

If a,b,c,d are in continued proportion,then (a^(3)+b^(3)+c^(3))/(b^(3)+c^(3)+d^(3))=(i)(a)/(b)(ii)(b)/(c)(iii)(c)/(d)(iv)(a)/(d)

If a, b, c, d are in proportion, then a : b = c : d and written as a : b : : c : d . Which of the following is true?

If a,b,c,d are four positive numbers that (i)((a)/(b)+(b)/(c))((c)/(d)+(d)/(e)) =4.sqrt((a)/(c))(iii)(a)/(b)+(b)/(c)+(c)/(d)+(d)/(e)+(e)/(a) =(1)/(5)

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