Question

The product of two numbers is 12960 then the sum of those numbers is 6 what are the two numbers?

Answer 1

Given : -

The product of two numbers is 12960 then the sum of those numbers is 6 what are the two numbers ?

To find : -

What are the two numbers ??

Solution : -

Let the first number be x then other number be y

According to the given condition

Product of two number = 12960

=> xy = 12960

=> y = 12960/x

Now,

Sum of two number = 6

=> x + y = 6

putting the value of y

=> x + 12960/x = 6

=> x² + 12960/x = 6

=> x² + 12960 - 6x = 0

=> x² - 6x + 12960 = 0

Applying quadratic formula to solve this equation

a=1 b=-6 c=12960

$\implies\sf x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$\implies\sf x=\frac{-(-6)\pm\sqrt{(-6)^2-4\times{1}\times{12960}}}{2\times{1}}$

$\implies\sf x=\frac{6\pm\sqrt{36-51840}}{2}$

$\implies\sf x=\frac{6\pm\sqrt{51804}}{2}$

$\implies\sf x=\frac{6\pm{227.6}}{2}$

$\implies\sf x=\frac{233.6}{2},\frac{-221.6}{2}$

=> x = 116.8 , - 110.8

Substitute the value of x in equation

x+y=6

if x = 116.8

=> x + y = 6

=> 116.8 + y = 6

=> y = 6 - 116.8 = -110.8

or

if x = -110.8

=> x + y = 6

=> -110.8 + y = 6

=> y = 6 + 110.8

=> y = 116.8

Case : 1

Required numbers

x = 116.8

y = -110.8

Case : 2

Required numbers

x = -110.8

y = 116.8