Answer :

Let the present age of boy and his brother be x years and (25 – x) years

According to given question


x(25 – x) = 126


25x – x2 = 126


x2 – 25x + 126 = 0


Using the splitting middle term – the middle term of the general equation is divided in two such values that:


Product = a.c


For the given equation a = 1 b = – 25 c = 126


= 1.126 = 126


And either of their sum or difference = b


= – 25


Thus the two terms are – 18 and – 7


Sum = – 18 – 7 = – 25


Product = – 18. – 7 = 126


x2 – 18x – 7x + 126 = 0


x (x – 18) – 7(x – 18) = 0


(x – 18) (x – 7) = 0


x = 18 or x = 7


x = 18 (Present age of boy cannot be less than his brother)


if x = 18


The present age of boy is 18 years and his brother is (25 – 18) = 7years


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