Question

difference of two numbers is 8 and their product is 384. what are the numbers​

Answer 1

Question

Difference of two numbers is 8 and their product is 384. What are the numbers ?

Answer

$\star \: \boxed {x = 24}$

$\star \: \boxed {y = 16}$

$\bf \longrightarrow{Step \: wise \: Explanation }$

Given that the difference between two numbers is 8 , this means one number must be 8 units greater than the other number.

So , Let the required number be x and y .

Such that :

x = 8 + y

According to the question

$\sf \: x \times y = 384$

Substitute the value of x

$\leadsto\sf(8 + y)y = 384 \\ \sf \: y ^{2} + 8y - 384 = 0 \\ \sf \: y ^{2} + 24y - 16y - 384 = 0 \\ \sf y(y + 24) - 16(y + 24) = 0 \\ \sf(y + 24)(y - 16) = 0 \\ \sf y = - 24 \: or \bf \: y = 16$

So , we got y = 16

Now , we know that x = 8 + y

$\boxed {x = 8 + 16} \\ \bf x = 24$

Thankyou