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The sum of the reciprocals of two consecutive integers is 9/20. Determine the consecutive integers algebraically.

I got the formula down, in the answer sheet it says the answers are 4 and 5.

The sum of the reciprocals of two consecutive integers is 9/20. Determine the consecutive-example-1

2 Answers

6 votes
The answer is 2 1/5.
User Weibeld
by
7.7k points
5 votes

Answer : The two consecutive integers are, 4 and 5

Step-by-step explanation :

Let the two consecutive number be, x and (x+1)

The sum of the reciprocals of two consecutive integers is 9/20.

The expression will be:


(1)/(x)+(1)/(x+1)=(9)/(20)

Now solving the term 'x', we get:


(x+1+x)/((x)(x+1))=(9)/(20)


(2x+1)/(x^2+x)=(9)/(20)


20(2x+1)=9(x^2+x)


40x+20=9x^2+9x


9x^2-31x-20=0

We are solving the quadratic equation by middle term splitting.


9x^2-36x-5x-20=0


9x(x-4)+5(x-4)=0


(9x+5)(x-4)=0


(9x+5)=0\text{ and }(x-4)=0


x=(-5)/(9)\text{ and }x=4

We are neglecting the value of
x=(-5)/(9)

Thus we are taking x = 4

When x = 4 then (x+1) = (4+1) = 5

Thus, the two consecutive integers are, 4 and 5

User James Robinson
by
8.5k points

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