Analytic method

1. The word analytic is derived from the word ‘analysis’ which means breaking up
or resolving a thing in to its constituent elements.
This method is based on analysis and therefore in this method we break up
the problem in hands in to its constituent parts so that it ultimately gets
connected with something obvious or already known.
In this process we start with what is to be find out (unknown) and then think
of further step and possibilities which may connect with the known and find
out the desired result.

2. if a2+b2=7ab prove that 2log (a+b) = 2log3+loga+logb
Proof:
To prove this using analytic method, begin from the
unknown.
The unknown is 2log (a+b) = 2log3+loga+logb
Now, 2log (a+b) = 2log 3+ log a+ log b is true
If log (a+b)2 = log 32 + log a + log b is true
If log (a+b)2 = log 9 + log ab is true
If log (a+b)2 = log 9ab is true
If (a+b)2 = 9ab is true
if a2+b2=7ab which is known and true
Thus if a2+b2= 7ab prove that 2log (a+b) =
2log3+loga+logb

3. If a/b = c/d, then P.T (ac +4b2 )/ bc =( 𝒄𝟐
+ 4bd)/dc.
Solution: To prove this using analytic method, begin from the
conclusion. The unknown is
(ac + 4b2)/bc = (c2+4bd)/dc.
=>( ac+ 4b2)/b = (c2+4bd)/d. is true
=> d(ac+ 4b2 ) = b(c2+4bd) is true
=> dac+ 4db2 = bc2+4b2d.
=> dac = bc2.
da = bc.
=> a/b = c/d.
 This type of the solution of the problem can be easily
obtained by analysis..

4. • Develops the power of thinking and reasoning
• It leaves no doubt in the minds of the students as every
step is justified.
• Helps in a clear understanding of the subject because the
students have to go through the whole process
themselves.
• It is a psychological method
• Develops originality and creativity among the students.

5. • Students participation is maximum
• It helps in developing the spirit of enquiry and
discovery among the students.
• No cramming is necessary in this method each
step has its reason and justification
• Students take active role in the learning process
resulting in longer retention and easier longer of
what they learn.
• It develops self- confidence in the students as
they tackle the problems confidently and
intelligently.

6. • Time consuming and lengthy method ,so it is uneconomical
• With this method it is difficult to acquire efficiency and speed
• This method may not be suitable for all topics of mathematics.
• Facts are not presented in a neat and systematic manner.
• Does not find favour with all the students because below average students
fail to follow this method.
• Every teacher cannot use this method effectively