Question

Give two or more examples of the following statements :-
a) If 'a' is odd, sum of other two numbers is ^a2 and their difference is 1.
b) If 'a' is even , sum of two numbers is ^a2/2 and their difference is 2.
( If 'a','b',and 'c' are three natural numbers with 'a' as the smallest of them.)

Answer 1

Answer :

We can have a , b and c , where 'a' , ' b ' and 'c' are three natural numbers with 'a' as the smallest of them . As :

a ) If 'a' is odd, sum of other two numbers is a² and their difference is 1 .

So,

1 ) a = 3 ( odd number )

And

b = 4 And c = 5 , Here their difference = 1
And

a² = 3² = 9
And
b + c = 4 + 5 = 9

2 ) a = 5 ( odd number )

And

b = 12 And c = 13 , Here their difference = 1
And

a² = 5² = 25
And
b + c = 12 + 13 = 25

3 ) a = 7 ( odd number )

And

b = 24 And c = 25 , Here their difference = 1
And

a² = 7² = 49
And
b + c = 24 + 25 = 49

b ) If 'a' is even , sum of two numbers is $\frac{a^2}{2}$ and their difference is 2.
So,

1 ) a = 4 ( even number )

And

b = 3 and c = 5 , Here their difference = 2
And
$\frac{a^2}{2}=\frac{4^2}{2}=\frac{16}{2}=\mathbf{}\mathbf{8}$
And
b + c = 3 + 5 = 8

2 ) a = 8 ( even number )

And

b = 15 and c = 17 , Here their difference = 2
And
$\frac{a^2}{2}=\frac{8^2}{2}=\frac{64}{2}=\mathbf{}\mathbf{32}$
And
b + c = 15 + 17 = 32

3 ) a = 10 ( even number )

And

b = 24 and c = 26 , Here their difference = 2
And
$\frac{a^2}{2}=\frac{{10}^2}{2}=\frac{100}{2}=\mathbf{}\mathbf{50}$
And
b + c = 24 + 26 = 50