Question

Two numbers differ by 4 and their product is 192. Then the numbers are 12, 16.

• A. True
• B. False

Answer 1

The correct option is A True

Given,

$a-b=4$......(1)

$ab=192$

We know that,

$(a+b{)}^2+(a-b{)}^2=4ab$

$(a+b{)}^2+4^2=4(192)$

$(a+b{)}^2=784$

$\therefore a+b=28$....(2)

Adding (1) and (2), we get:

$2a=32$

$\Rightarrow a=16$

Substituting value of $a$ in (1), we get:

$16-b=4$

$\therefore b=12$

So, $a=16,b=12$

Hence, the given statement is true.