Q12 of 168 Page 7

Divide 12 into two parts such that the sum of their squares is 74.

Let the first number be ‘X’, so the other number will be ’(12–X)’.


∵ X2 + (12 – X)2 = 74


X2 + 144 + X2 – 24X = 74


On simplifying further,


2X2 – 24X + 70 = 0


X2 – 12X + 35 = 0


On applying Sreedhracharya formula







∴ X = 5 or X = 7.


Then other numbers will be (12–X) = {12–5} & {12–7} i.e., 7 or 5.


∴ The number 12 is divided into two parts namely 5 & 7.


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