Answer to Question #199457 in Algebra for Curly

Question

The sum of two positive number is 14 and difference between their squares is 56. What is the sum of their squares?

Answer 1

Let the numbers be a and b,

a + b = 14     

a² – b² = 56    

 (a² – b²) = (a + b) (a – b)

The difference between numbers  squares is 56.

 (a + b) (a – b) = 56

The sum of two positive number is 14,

so  

(a + b) = 14, (1)

(a – b) = 56 /(a+b)= 56/14= 4     (2)

From formula (2) we have:

a=4+b

From formula (1) we have:

(4 + b + b) = 14

2b=14 - 4=10

b=5,

a=4 + b=4+5=9,

a = 9,  b = 5

Sum of squares =a² + b² = 9² + 5² = 81 + 25 = 106 

Answer:

106