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प्रश्न
The sum of the squares of two positive integers is 208. If the square of the large number is 18 times the smaller. Find the numbers.
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उत्तर
Let the two numbers be x and y, y being the bigger number.
From the given information,
x2 + y2 = 208 ...(i)
y2 = 18x ...(ii)
From (i), we get y2 = 208 – x2
Putting this in (ii), we get,
208 – x2 = 18x
⇒ x2 + 18x – 208 = 0
⇒ x2 + 26x – 8x – 208 = 0
⇒ x(x + 26) – 8(x + 26) = 0
⇒ (x – 8)(x + 26) = 0
⇒ x can't be a negative number, hence x = 8
⇒ Putting x = 8 in (ii), we get y2 = 18 × 8 = 144
⇒ y = 12, since y is a positive integer
Hence, the two numbers are 8 and 12.
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