If the difference of two numbers is 5 and their product is 84, then the numbers 

Correct option is (B) 12, 7

Let the numbers are a and b.

\(\therefore\) Their difference = a - b

And product = ab

\(\therefore\) a - b = 5    _____________(1)

& ab = 84     _____________(2)  (Given)

Now, \((a+b)^2=(a-b)^2+4ab\)

\(=5^2+4\times84\)

= 25+336

= 361 \(=19^2\)

\(\therefore\) a+b = 19   _____________(3)

By adding (1) & (3), we obtain

(a - b) + (a+b) = 5+19

\(\Rightarrow\) 2a = 24

\(\Rightarrow\) a = \(\frac{24}2\) = 12

\(\therefore\) b = 19 - a       (From (3))

= 19 - 12 = 7

Hence, the required numbers are 12 and 7.

Correct option is B) 12, 7