SOLUTION: The sum of the radii of two circles is equal to 17 centimeters. The sum of the areas of these two circles equals the area of a circle whose radius is 13 centimeters. Find the radii

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let x and y equal the two radii ... x+y=17 ... y=17-x ... pi(x^2)+pi(y^2)=pi(13^2) ... x^2+(17-x)^2=13^2

x^2+17^2-34x+x^2=13^2 ... 2x^2-34x+120=0 ... x^2-17x+60=0 ... (x-5)(x-12)=0

x=5 or x=12, so y=12 or y=5 ... the two radii are 5 and 12