Q. 95.0( 2 Votes )

The difference of squares of two natural numbers is 45. The square of the smaller number is four times the larger number. Find the numbers.

Answer :

Let the larger number be ‘X’, so the smaller number will be ‘Y’.


X2 – Y2 = 45 ––––– (i)


4X = Y2 –––––– (ii)


On simplifying further,


Putting the value of Y2 = 4X from equation –––––– (ii)


X2 – 4X = 45


X2 – 4X – 45 = 0


On applying Sreedhracharya formula







X = – 5 or 9


X = 9 (Only natural number, as given in the question)


Y=√(4*9)


Y = 6


The numbers are 9 & 6.


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