Question

4 numbers in a square is marked on the calendar.

Add the squares of number pairs in angle to angle. Find out the difference of these sums?

4² + 12² = 160

11² + 5² = 146

160 – 146 = 14

(i) In the same was mark other 4 numbers and work out the questions.

(ii) Explain the reason on the basis of algebra that in all the squares we get the difference 14.

Answer 1

(i)

5² + 13² = 25 + 169 = 194

12² + 6² = 144 + 36 = 180

194 – 180 = 14

(ii) Let the first number in the square is x

[x² + (x + 8)²] – [(x + 7)² + (x + 1)²]

[x² + x² + 16x + 64] – [x² + 14x + 49 + x² + 2x + 1]

= 14