Q9 of 168 Page 7

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.

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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