Question

33. यदि a तथा b ऐसे धन पूर्णाक हैं कि a2-b2 = 19 है, तो
a का मान होगा -
(a) 19 (b) 20 (c)9 (d) 10​

Answer 1

Given:

a and b are positive integers such that a² - b² = 19

To find:

The value of a

Solution:

It is given,

a² - b² = 19

⇒ (a + b)(a - b) = 19 ...... [since a² - b² = (a + b)(a - b)]

since 19 is a prime number therefore only factor of 19 can 19 and 1

⇒  (a + b)(a - b) = 19 × 1 ..... (i)

• a and b are two positive integers i.e., a, b > 0
• (a + b) > 0 and (a - b) > 0
• Also, the sum of 2 positive integers will be more than the difference of that 2 positive integers.

So, from (i), we can write as:

(a + b) = 19 ..... (ii)

and

(a - b) = 1 .... (iii)

Now, on adding (ii) & (iii), we get

a + b = 19

a - b = 1

+

----------------

2a = 20

---------------

∴ a = $\frac{20}{2}$ = 10

Thus, the value of a will be → option (d) → 10

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