Find the consecutive odd natural numbers some of whose square is 970
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Answer:
21, 23
( 21² + 23² = 441 + 529 = 970 )
Step-by-step explanation:
Let the two consecutive odd natural numbers be 2n-1 and 2n+1, where n≥1 is an integers.
The sum of their squares is 970
=> (2n-1)² + (2n+1)² = 970
=> 4n² - 4n + 1 + 4n² + 4n + 1 = 970
=> 8n² = 968
=> n² = 121
=> n = 11.
Therefore the two consecutive odd natural numbers are
2n-1 = 21 and 2n+1 = 23.
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