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The square of the sum of two numbers is 144 and the sum of their square is 180, find the numbers

 Jan 26, 2020
 #1
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Let the two numbers be x and y.

The square of x+y is x^2+2xy+y^2 and that is 144

The sum of x^2 and y^2 is 180. 

So you can get from substituting the second equation to the first and you get

180+2xy=144

So 2xy= -36

xy= - 18

And x+y = 12 or -12

because 12^2 or -12^2 is 144.

(x-y)^2 is x^2-2xy+y^2 which is 180 +36 or 216

So x-y equals 6sqrt6, or -6sqrt6. 

Adding and dividing be 2

gives x = 6 + 3sqrt6 and y= 6 - 3sqrt6

And your done

By: GF

 Jan 26, 2020

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