For your first discussion please tell us a problem that you

For your first discussion please tell us a problem that you solved and how George Polya’s guidelines applied. Do not feel that you need to use one of the problems from the textbook. Math is everywhere and being applied everyday, even if we do not realize it is math. Please outline the specific problem, your solution and how the specific problem solving guidelines were applied. Be sure to carefully tell us how you applied each of the guidelines to your problem.

Solution

Polya`s approach to solve a problem is to follow these steps :

(i) Understanding the problem

(ii) Devise the plan

(iii) Implement the plan

(iv) Looking back

For example we take the following problem :

:\" Find two numbers so that their product is 56 and their sum is 15.\"

So here we first start it by side by side translating it as :

In English                           In algebraic language

Find two numbers                        a and b

whose sum is 15                         a+b= 15              ........(i)

whose product is 56                    ab = 56

Now next approach is to get a formula for it so that to use this given information in it (device a plan) and that is :

(a-b)^2=(a+b)^2 -4ab

Now we put related given values in this formula and simplify that is the part of Poyla`s third step of processing,

so (a-b)^2= (!5)^2 - 4(56) = 225 - 1224= 1

or a-b = 1 .............(ii)

Now in order to get values of a and b separately, we add both equations (i) and (ii), so that y terms are eliminated and we get

2a=15+1=16

or a= 8

and thus by first equation a+b=15

or 8+b = 15

or b= 15- 8 = 7

so our two numbers required are 7 and 8.

And now Poyla`s last step : \" Looking back \"

i.e. cross checking the answer:

so if we put a=8 and b= 7 in first equation, we get a+b = 8+7 = 15

that is true, so our answer is correct.

This is the Polya` s approach to solv e a math problem.