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Let their ages be x and y:

x+y = 51 => y = 51-x

xy = 648

x(51-x) = 648

51x-x2-648 = 0

x2-51x+648 = 0

(x-24)(x-27) = 0

x = 24 or x = 27

So their ages were 24 and 27

Check: 24+27 = 51 and 24*27 = 648

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