Question

Express (19 square) as the sum of two consecutive integers

Answer 1

Answer:

19² = 180 + 181

Step-by-step explanation:

Given:- The given number is 19².

To find:- Express 19² as the sum of two consecutive integers.

Solution:-

We know that, when n is odd, n² = $\frac{n^{2}+1 }{2} + \frac{n^{2} -1}{2}$ , this is the sum of two consecutive integers.

19 is an odd number as it is not a multiple of 2.

∴ 19² = ( (19² -1) ÷ 2) + ( (19² + 1) ÷ 2)

         =  (((361) - 1) ÷ 2) + (((361) + 1) ÷ 2)

         = (360 ÷ 2) + (362 ÷ 2)

         = 180 + 181

180 and 181 are the two consecutive numbers.

Therefore, 19² = 180 + 181.

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