Question

express 10² as the sum of consecutive odd natural numbers ​

Answer 1

Step-by-step explanation:

let the two consecutive odd positive integer be X, x+2

according to question

x+x+2 = 10*10

2x+2 = 100

2x = 100-2

2x = 98

x = 98/2

x = 49

now X = 49

x+2= 49 + 2

= 51

Answer 2

Answer:

Step-by-step explanation:

Any odd integer is of form

4q+1 or 4q+3 for any integer q.

Now, 4q+1 and 4q+3 are consecutive odd numbers as their diff. is 2.

Sum of consecutive odd numbers=

(4q+1) + (4q+3) =10^2=100 -given

Therefore, 8q+4=100

8q=96

Hence, q=12

=> 4q+1=49

=> 4q+3=51

Therefore, the two odd consecutive integers whose sum is 10^2 i.e. 100 are 49 and 51.