Question

The sum of two numbers is 8 and the difference of their squares is 32. Find the numbers.

Answer 1

Let two no's be x & y

x + y = 8            ...(i)

x² - y² = 32       

(x + y) (x - y) = 32

8 (x - y) = 32

x - y = 4           ...(ii)

Adding equation (i) & (ii)

x + y = 8  
x - y = 4 
2x = 12

x = `12/2`

x = 6

From equation (i)

6 + y = 8

y = 8 - 6

y = 2