The sum of two positive numders is 18 and the sum their squares is 180.
Find the numbers.
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by the conditions given in the question we get equations
x+y=18. ... (1)
x^2+y^2=180
(x+y)^2=x^2+y^2+2xy
(18)^2=180+2xy
324-180=2xy
2xy=144
(x-y)^2=x^2+y^2-2xy
(x-y)^2=180-144
(x-y)^2=36
x-y=6. .... (2)
by adding equations (1)&(2)
2x=24
x=12
y=6
so the numbers are 12&6