Question

The difference of two numbers is 3 and the difference of their squares is 69. Find the numbers.

Answer 1

Let one number = x

$\therefore$ Second number = x + 3

[$\because$ Difference of two numbers is 3]

According to the statement :

$(x+3{)}^2-(x{)}^2=69\Rightarrow (x{)}^2+(3{)}^2+2\times x\times 3-x^2=69\Rightarrow x^2+9+6x-x^2=69\Rightarrow 6x=69-9\Rightarrow 6x=60\Rightarrow x=\frac{60}{6}\Rightarrow x=10$

$\therefore$ One number = 10

Second number = x + 3 = 10 + 3 = 13.