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Please answer fast!!!!!! The sum of the reciprocals of two consecutive even integers is 9/40. This can be represented by the eq
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Please answer fast!!!!!!
The sum of the reciprocals of two consecutive even integers is
9/40. This can be represented by the equation shown.
1/x+1/x+2=9/40
Use the rational equation to determine the integers. Show all work.
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Mathematics
4 years
2021-07-25T20:14:54+00:00
2021-07-25T20:14:54+00:00 1 Answers
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Answer:
8 and 10
Step-by-step explanation:
Given
9(x² + 2x) = 40(2x + 2) ← distribute both sides
9x² + 18x = 80x + 80 ( subtract 80x + 80 from both sides )
9x² – 62x – 80 = 0
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 9 × – 80 = – 720 and sum = – 62
The factors are – 72 and + 10
Use these factors to split the x- term
9x² – 72x + 10x – 80 = 0 ( factor the first/second and third/fourth terms )
9x(x – 8) + 10(x – 8) = 0 ← factor out (x – 8) from each term
(x – 8)(9x + 10) = 0
Equate each factor to zero and solve for x
x – 8 = 0 ⇒ x = 8
9x + 10 = 0 ⇒ 9x = – 10 ⇒ x = –
x is an integer , then x = 8 and x + 2 = 8 + 2 = 10
The integers are 8 and 10