Question

(a) Take a square of 4 numbers and multiply angle to angle and find the difference. Is the difference the same when 4 numbers are taken from the comers in any square?

(b) Explain the reason by using the principle of algebra.

(c) Take a square of 9 numbers multiply angle to angle and find the difference. Explain on the basis of algebra.

Answer 1

(a)

17 × 12 – 11 × 18 = 204 – 198 = 6 We get the same difference

(b) Take the square with the numbers as follows.

(n + 6) ( n + 1) – n (n + 7)

(n² + 7) (n + 6) – (n² + 7n) = 6

(c)

(n + 5) (n – 5) – (n – 7) (n + 7)

(n² – 5²) (n² – 7²)

= 7² – 5²

= 49 – 25 = 24