Question

The difference of two numbers is 8, and the sum of the squares of these two numbers is 320. What are the numbers ?​

Answer 1

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Answer 2

Given :

The difference of two numbers is 8, and the sum of the squares of these two numbers is 320.

To find :

What are the numbers ?​

Solution :

Let x and y be the numbers.

So we get

$x-y=8\\x^{2} +y^{2} =320$    

Now solve first equation for x we get

$x=8+y$

Now substitute the value of x in the second equation we get

$(8+y)^{2}+y^{2}=320\\y^{2} +16y+64+y^{2} =320 \\2y^{2}+16y-256=0$

Now factorize the above equation we get

$(y+16)(y-8)=0$

Solving for y we get

$y= -16 , y= 8$

Hence, the numbers are (-16 and 8)