Question

The sum of two numbers is 16 and the sum of their squares is 113. find the numbers

Answer 1

Let x be one of these numbers and y be the other. 

x+y =15 --------------- Eq(1) 
x^2 + y^2 = 113 ---- Eq(2) 

From Eq(1): y=15-x ----------Eq(3) 

Sub Eq(3) into Eq(2): 
x^2 + (15-x)^2 = 113 
x^2 + (225 - 30x + x^2) = 113 ----- Using (a-b)^2 = a^2-2ab+b^2 
x^2 + 225 - 30x + x^2 = 113 
x^2 + x^2 - 30x + 225 -113 = 0 
2x^2 - 30x + 112 =0 
x^2 - 15x + 56 = 0 
(x-7)(x-8) = 0 
x= 7 or x = 8 

When x=7, y=15-7 =8 
When x=8, y=15-8 =7 

Therefore, the 2 numbers are 7 & 8

Answer 2

Answer:

Step-by-step explanation:

Given :-

The sum of two numbers is 16 and the sum of their squares is 113.  

To Find  :-

The Numbers

Solution :-

Let the 1st number be x .

And the second number be (15 - x).  

According to the Question,

⇒ x² + (15 - x)² = 113

⇒ x² + 225 + x² - 30x = 113  

⇒ 2x² - 30x + 112 = 0  

⇒ x2 - 15x + 56 = 0  

⇒ (x - 7) (x - 8) = 0  

⇒ x = 7 or x = 8.  

Hence, the required numbers are 7 and 8.