Home
Class 10
MATHS
Given, (a)/(b) = (c)/(d), prove that : ...

Given, `(a)/(b) = (c)/(d)`, prove that :
`(3a - 5b)/(3a + 5b) = (3c - 5d)/(3c + 5d)`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • RATIO AND PROPORTION (INCLUDING PROPERTIES AND USES)

    ICSE|Exercise Exercise 7(D)|27 Videos

  • RATIO AND PROPORTION (INCLUDING PROPERTIES AND USES)

    ICSE|Exercise QUESTIONS|30 Videos

  • RATIO AND PROPORTION (INCLUDING PROPERTIES AND USES)

    ICSE|Exercise Exercise 7(B)|17 Videos

  • RATIO AND PROPORTION

    ICSE|Exercise MULTIPLE CHOICE QUESTION|61 Videos

  • REFLECTION

    ICSE|Exercise QUESTION|1 Videos

Similar Questions

Explore conceptually related problems

If (7a + 8b)/( 7c + 8d) = (7a - 8b)/(7c - 8d), prove that : (i) a:b=c:d (ii) (4a - 5b)/(4c - 5d)= (3a + 4b)/(3c + 4d)

If a : b = c : d , prove that : (6a + 7b) (3c - 4d) = (6c + 7d) (3a - 4b) .

if (8a - 5b)/(8c - 5d) = (8a + 5b)/(8c + 5d) , prove that (a)/(b) = (c)/(d) .

if a : b = e : d , show that : 3a + 2b : 3a - 2b = 3c + 2d : 3c - 2d .

Subtract : 3a - 5b + c + 2d from 7a - 3b + c - 2d

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 :

(-3/5)^(-1) = (a)3/5 (b) 5/3 (c) -5/3 (d) -3/5

If a/b=4/3, then the value of (6a+4b)/(6a-5b) is (a) -1 (b) 3 (c) 4 (d) 5

Simplify : (5a + 5b - c)(2b - 3c)

if a , b , c and d are in proportion, prove that : (i) (a-b)/(c-d)= sqrt((3a^(2) + 8b^(2))/(3c^(2) + 8d^(2))) (ii) ((5a^(2) + 12c^(2))/(5b^(2) + 12d^(2))) = sqrt((3a^(4) - 7c^(4))/(3b^(4) - 7d^(4)))