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Question
The difference of the square of two natural numbers is 45. The square of the smaller number is 4 times the larger number. Determine the numbers.
Solution
Let these two numbers be X and Y, Y being the bigger number. Then as per the question,
Y2 - X2 =45 ..... (i)
X2 = 4Y ..... (ii)
From (i), we get X2=Y2- 45, Putting this in (ii), we get
Y2 - 45 - 4Y = O
⇒ Y2 - 4Y- 45 = 0
⇒ Y2 - 9Y + 5Y - 45 = 0
⇒ Y (Y - 9) + 5( Y - 9) = 0
⇒ (Y-9) (Y+S) = 0
⇒ Y can't be a negative number and hence Y=9
⇒ Putting Y = 9 in (ii), we get X2 = 4 x 9=36
⇒ X = 6
Hence numbers are 6 and 9.
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