Question

The sum of 2 numbers is 28 and difference of their squares is 112.Find the numbers

Answer 1

Answer:

Numbers are 16 and 12

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Step-by-step explanation:

Let the numbers be x and y

Given,

$x+y=28$  

$x^{2} -y^{2} = 112$

$Using \ formula : a^{2} -b^{2} =(a-b)(a+b)$

$\frac{x^{2} -y^{2} }{x+y} =\frac{112}{28}$

⇒ $\frac{(x+y)(x-y)}{x+y} = 4$

$x-y=4$

Now,

On adding both the equations :

$x+y=28$  

$x-y=4$

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2x = 32

x = 16

Keeping the value of x in any of the equations

x + y = 28

16 + y = 28

y = 28 - 16

y = 12