Q. 1 B3.8( 4 Votes )
Mark four numbers forming a square in a calendar:
Add the squares of the diagonal pair and find the difference of these sums:
42 + 122 = 160
112 + 52 = 146
160 – 146 = 14
Explain using algebra, why the difference is 14 always.
Answer :
Let’s use algebra to see this.
Taking the first number in the square as x, the others can be filled as below
the squares of diagonal are
x2 and (x+8)2
(x+7)2 and (x+1)2
Add the squares of the diagonal pair
x2 + (x+8)2
= x2 + (x2+82+2
[Using identity 
= 
+ 
+ 2
]
= 2x2 + 64+16
Add the squares of the other diagonal pair
= (x+1)2+(x+7)2
= (x2 +1 +2
(x2+72+2
= (x2 +1 +2
(x2 +49 +14
)
= 2x2 +16
+ 50
find the difference of these sums:
= (2x2 + 64+16
- (2x2 +16
+ 50)
= 2x2 + 64+16
- 2x2 -16
- 50
= 64-50
= 14
Hence the difference is 14, we can take any number as x; which means this holds in any part of the calendar.
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