If
5 +2
/5−2
=
7
/5
, use properties of proporation to find i) ∶ ii) ²+y²/x²-y²
Answers
Answer:
Let the third proportional to (x² - y²) and (x - y) be P.
Therefore, (x² - y²), (x - y) and P are in proportion.
=> (x² - y²) : (x - y) = (x - y) : P
=> (x² - y²)/(x - y) = (x - y)/P
=> P = (x - y)²/(x² - y²)
=> P = (x - y)(x - y)/(x + y)(x - y)
=> P = (x - y)/(x + y).
Therefore, the third proportional to (x² - y²) and (x - y) is (x - y)/(x + y).
7.8K viewsView 9 Upvoters
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Ranjeet R Tiwari, B.Sc. Physics & Mathematics, Magadh University (2014)
Answered March 10, 2018 · Author has 57 answers and 95K answer views
If A,B and C are are in proportion then
A/ B = B/C
By using this you can solve the above question
I.e third term = square of second term / first term
= (X-Y )^2 / X^2 - Y^2
But X^2 - Y^2 can be factoriesed as (X-Y)(X+Y)
So third term will be (X-Y)/ (X+Y)
This is the required answer
=>
3.5K viewsView 1 Upvoter
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Dhrubajyoti Bhattacharjee, BSMS(Dual) Mathematics from National Institute of Technology, Agartala (2023)
Answered May 9, 2018 · Author has 605 answers and 536.8K answer views
Let, the required answer be p.
Then, we have,
(x^2 - y^2)/(x-y) = (x-y)/p
=> p = (x^2 - y^2)/(x-y)^2 .
Now, if x & y are distinct no.s, we get,
p = (x+y)/(x-y) .
Hope, it'll help..
Thank You!
5.6K viewsView 3 Upvoters
Vikas Singh, L'hospitals at your rescue
Answered October 4, 2016 · Author has 148 answers and 179.2K answer views
The third proportion to 2 numbers a, b is c iff a:b::b:c
So lets assume c is the third proportion to x^2-y^2 and x-y then
x^2-y^2 : x-y :: x-y : c
=> (x^2-y^2) / (x-y) = (x-y)/c
=>c = (x-y)^2/(x^2-y^2)
4K viewsView 1 Upvoter
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