Question
Download Solution PDFThe product of two consecutive odd numbers is 6723. What is the greater number?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The product of two consecutive odd numbers is 6723.
Formula used:
(a + b)(a - b) = a2 - b2
Calculation:
Let the smaller number be 2x - 1 and the greater number be 2x + 1.
(2x - 1)(2x + 1) = 6723
⇒ (2x)2 - 12 = 6723
⇒ 4x2 - 1 = 6723
⇒ 4x2 = 6724
⇒ x2 = 6724 / 4
⇒ x2 = 1681
⇒ x = √1681
⇒ x = 41
The greater number (2x + 1):
2x + 1 = 2(41) + 1
⇒ 82 + 1 = 83
∴ The greater number is 83.
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