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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