Question

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 1

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 x 9)

∴ Y = 6

∴ The numbers are 9 & 6.