1) interesting questions on expansion:

If it is given that ::    ( a^2-b^2)=c

   

Then find the value of 'a'  and 'b'.

Solution;

(a^2-b^2) * 1=c*1                  (multiplying 1 both sides) 

(a^2-b^2)=c*1

(a+b)(a-b)=c*1

Therefore:

(a+b)=c -----------------------------------(1st eq.)

(a-b)=1------------------------------------(2nd eq.)

(Adding eq 1 and 2 )

a+b+a-b=c+1

2a=c+1

a=c+1/2

(Substracting eq 2 from 1)

a-a+b+b=c-1

2b=c-1

b=c-1/2

        

Thus:

a=(c+1)/2 .         And .             b=(c-1)/2

Characteristics of these formulas:

1) .When the value of c is even then the value of a and b will be in decimals.

2).  When the value of c is odd then the value of a and b will be an real number.

Note: this formula is applicable for specific numbers .

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