Q. 3 B4.0( 3 Votes )

Take nine numbers forming a square in a calendar and mark the four numbers at the corners.



Multiply the diagonal pairs and find the difference of these products.

3 × 19 = 57

17 × 5 = 85

85 – 57 = 28

Explain using algebra, why the difference is always 28 (It is convenient to take the number at the centre as x).

Answer :

Let’s use algebra to see this.

Taking the first number in the square as x, the others can be filled as below



Multiply the diagonal pairs


(x)(x+16)


= x2+16x


Other diagonal product


(x+14)(x+2) [using identity (x+y)(u+v)= xu+xv+yu+yv]


= x2+2x+14x+28


= x2+16x+28


Difference of these products





=(x2+16x+28) - (x2+16x)


=x2+16x+28 - x2-16x


= 28


Hence the difference is 28, we can take any number as x; which means this hold in any part of the calendar.


We can take x at the center, but this will complicate our calculations.



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