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child 1 = a

child 2 = b

a + b = 23

a x b = 132

a = 23 - b

(23 - b) x b = 132

-b^2 + 23b - 132 = 0

Now it has become a quadratic, you can use the quadratic rule, but i'll bore you no longer

child b = 11 or 12

So The first born child would be 12 years old and the second born would be 11 years old

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12y ago

What else can I help you with?