Question

If a and b are positive integers such that a2-b2=19 then the value of a is

Answer 1

value of a........ is
.......
19

Answer 2

Answer:

The value of x is 10.

Step-by-step explanation:

Let a and b are positive integers such that

$a^2-b^2=19$

$(a+b)(a-b)=19$        $[\beause a^2-b^2=(a+b)(a-b)]$

The positive factors of 19 are 1 and 19.

$(a+b)(a-b)=19\times 1$           .... (1)

Since a and b are positive integer and the difference of their squares is 19, therefore a>b.

The sum of two positive integer is more than the difference of those positive integers.

On comparing both sides of equation (1).

$a+b=19$            .... (2)

$a-b=1$                  .... (3)

Add equation (2) and (3).

$2a=20$

Divide both sides by 2.

$a=10$

Therefore, the value of x is 10.