The sum of 2 numbers is 6 and the difference between their squares is 12. What are these numbers?

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

Let the numbers be x and y :

==> x + y = 6 .......(1)

==> x^2 - y^2 = 12

We know that:

x^2 - y^2 = (x-y)(x+y)

==> (x-y)(x+y) = 12

But x+y = 6

==> 6*(x-y) = 12

Divide by 6:

==> x-y = 2 .........(2)

Now add (1) and (2) :

==> 2x = 8

==> x= 4

==> x+y = 6 ==> y= 6-x = 6-4 = 2

==> y= 2

Then the numbers are 2 and 4

william1941's profile pic

william1941 | College Teacher | (Level 3) Valedictorian

Posted on

We are given the sum of 2 numbers as 6 and the difference between their squares as 12.

Let's take the numbers as A and B.

A^2 - B^2 = 12

A + B = 6

Now A^2 - B^2 = 12

=> (A + B)(A-B) = 12

=> 6 (A-B) = 12

=> A- B = 2

So we have A+B = 6 and A-B =2

Add the two 2A = 8 => A = 4

So B = 6-4 = 2

Therefore the two numbers are 2 and 4.

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