Question

a) Mark four numbers forming a square in a calendar . Add the product of the diagonal

pair and find the difference of these products .

b) Is it same for all the squares of four numbers ?

c) Explain why this is so , using algebra .​

Answer 1

please give me 10 thank dear.

Answer 2

Given : Mark four numbers forming a square in a calendar .

To Find  : the product of the diagonal pair

the difference of these products .  

 Is it same for all the squares of four numbers

Solution:

Any four number in square in calendar will be of form

n          n + 1

n + 7     n + 8

n(n + 8)  - (n + 1)(n + 7)

= n²  + 8n  - ( n²  + 8n+ 7)

= - 7

Hence difference is constant

Yes ,  it same for all the squares of four numbers

for Example  

3     4

10    11

3 * 11 - 4 * 10  =  - 7

  8           9

  15         16

=8 * 16  -  9 * 15  =  - 7  

Learn More:

What are the two prime numbers whose product

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