Q1 of 137 Page 19

Determine two positive numbers whose sum is 15 and the sum of whose squares is minimum.

Let the two positive numbers be a and b.


Given: a + b = 15 … 1


Also, a2 + b2 is minima


Assume, S = a2 + b2


(from equation 1)


⇒ S = a2 + (15 – a)2


⇒ S = a2 + 225 + a2 – 30a = 2a2 – 30a + 225


⇒ = 4a - 30


⇒


Since, > 0 will give minimum value of S.


4a – 30 = 0


a = 7.5


Hence, two numbers will be 7.5 and 7.5.


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