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