The sum of two numbers is 18 and the sum of their squares is 170. How do you find the numbers?

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Answer 1 · 2016-03-05T19:02:54

7 and 11

$a) x+y=18$

$b) x^2+y^2=170$

$a) y=18-x$

replace y in b)

$b) x^2+(18-x)^2=170$

$x^2+324-36x+x^2=170$

$2x^2-36x+324-170=0$

$2x^2-36x+154=0$

Now you only need to use the quadratic form:

$x=(36+-sqrt(36^2-4*2*154))/(2*2)$

$x=(36+-sqrt(1296-1232))/(4)$

$x=(36+-sqrt(64))/(4)=(36+-8)/(4)$

$x=(36+8)/4 or x=(36-8)/4$

$x=11 or x=7$ and $y=18-11=7 or y=18-7=11$

So, the numbers are 7 and 11