Question 1: If , prove that:
Answer:
By componendo and dividendo
By componendo and dividendo
By componendo
Cross multiplying
Question 2: If , prove that:
.
Answer:
By Componendo
By Dividendo
Hence
[2000]
Answer:
By componendo and dividendo
By Alternendo
.
Answer:
By componendo and dividendo
.
Question 5: If ; prove that
Answer:
By componendo and dividendo
. Hence Proved.
Question 6:
Answer:
By componendo and dividendo
… … … … … … i)
Similarly
By componendo and dividendo
… … … … … … ii)
Adding i) and ii)
By componendo and dividendo
… … … … … … i)
Similarly
By componendo and dividendo
… … … … … … ii)
Adding i) and ii) we get
Question 7: If ; prove that
Answer:
By componendo and dividendo
Applying again componendo and dividendo
Simplifying
Hence Proved.
.
Answer:
By componendo and dividendo
Simplifying
Applying again componendo and dividendo
Simplifying
.
Answer:
Question 10: If are in continued proportion, prove that:
Answer:
Hence LHS = RHS. Hence Proved.
Hence LHS = RHS. Hence Proved.
Question 11: Using Properties of proportion, solve f :
Answer:
Applying componendo and dividendo
Squaring both sides
Applying componendo and dividendo
Squaring both sides
Applying componendo and dividendo
Applying componendo and dividendo
latex \displaystyle =5 $
Squaring both sides
. [2007]
Answer:
Applying componendo and dividendo
Squaring both sides
Applying componendo and dividendo once again
simplifying
Hence proved.
Question 13: Using the properties of proportion, solve for :
. [2013]
Answer:
Applying componendo and dividendo
Taking the square root of both sides
.
Answer:
Applying componendo and dividendo
Simplifying
Squaring both sides
Applying componendo and dividendo again
Simplifying
.
Answer:
Applying componendo and dividendo
Applying componendo and dividendo again
Simplifying