The difference is the square of two consecutive natural numbers is 65.what is the number?
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Answer :
- The numbers are 32 and 33
Given :
- The difference is the square of two consecutive natural numbers is 65
To find :
- The numbers
Solution :
- Let the number be x
- Other number be x + 1
Given, the difference is the square of two consecutive natural numbers is 65 so,
➠ (x + 1)² - x² = 65
➠ x² + 2x + 1 - x² = 65
➠ 2x = 65 - 1
➠ 2x = 64
➠ x = 64/2
➠ x = 32
Hence , The numbers are 32 and 33
Verification :
➠ (x + 1)² - x² = 65
➠ (32 + 1)² - (32)² = 65
➠ (33)² - 1024 = 65
➠ 1089- 1024 = 65
➠ 65 = 65
Hence verified
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