Q. 54.4( 9 Votes )

Divide 16 into tw

Answer :

Let the smaller part be x and the larger part be 16 – x.

Given:


2 × (Larger Part)2 = (Smaller Part)2 + 164


2 × (16 – x)2 = (x)2 + 164


2 × (256 – 32x + x2) = x2 + 164


512 – 64x + 2 x2 = x2 + 164


x2 – 64x + 512 – 164 = 0


x2 – 64x + 348 = 0


On factorizing the above equation,


Sum = -64


Product = 348


Therefore the two numbers satisfying the above conditions are -58 and -6.


x2 – 6x - 58x + 348 = 0


x(x – 6) - 58(x – 6) = 0


(x – 6) (x - 58) = 0


Solving first part,


x – 6 = 0


a = 6


Solving second part,


x - 58 = 0


x = 58


Since x is the smaller it cannot be greater than 16. Hence x cannot be 58


So the smaller part is x = 6


So the larger Part = 16 – 6


= 10


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