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प्रश्न
For two consecutive odd natural numbers, the square of bigger number exceeds the square of smaller number by 72. Find the two numbers.
उत्तर
Let the two consecutive even natural number be 2x + 1 and 2x + 3.
As per the given condition,
(2x + 3)2 - (2x + 1)2 = 72
⇒ 4x2 + 12x + 9 - [4x2 + 4x + 1] = 72
⇒ 4x2 + 12x + 9 - 4x2 - 4x - 1 = 72
⇒ 12x + 9 - 4x - 1 = 72
⇒ 8x = 64
⇒ x = `(64)/(8)`
⇒ x = 8
2x + 1 = 2(8) + 1 = 16 + 1 = 17 and 2x + 3 = 2(8) + 3 = 16 + 3 = 19
Hence, the numbers are 17 and 19.
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