Question

Two number differ by 4 and their product is 192. Find the numbers.

Answer 1

SOLUTION :  

Let the one  number be x and other number be (x - 4)  

A.T.Q  

x × (x -  4) = 192

x² - 4x = 192

x² - 4x - 192 = 0

x² - 16 x + 12x  - 192 = 0

[By middle term splitting]

x(x - 16) + 12 (x - 16) = 0

(x - 16) (x + 12) = 0

(x - 16) = 0  or (x + 12) = 0

x = 16  or  x = - 12

Case 1 :  

When x = 16 , then other number be  (x - 4)  = (16 - 4) = 12

Case 2 :  

When x = - 12 , then other number be  (x - 4)  = (- 12 - 4) = - 16

Hence, the two numbers are (16, 12)  and ( -12, - 16) .

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Answer 2

5 answers · Mathematics 

 Best Answer

One No. = x 
Other No. = y 

x - y = 4 
x = y + 4 ........ Eq. 1 

xy = 192 
y = 192 / x ..... Eq 2 


Sub y + 4 from Eq. 1 for x in Eq. 2: 

y = 192 / (y + 4) 
y(y + 4) = 192 
y² + 4y = 192 
y² + 4y - 192 = 0 
(y - 12)(y + 16) = 0 

If the product of two factors equals zero, then one or both factors equal zero. 

If y - 12 = 0, 
y = 12 

and 

x = 12 + 4 
x = 16 


If y + 16 = 0, 
y = - 16 

and 

x = - 16 + 4 
x = - 12 

The two numbers are 12 & 16 or - 12 & - 16. 

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