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Two consecutive integers are represented by x and x+2. The sum of the reciprocals of the integers is 29/420. Show your work and algebraically determine the two integers.

Jul 23, 2021

#1
+36430
+2

x and x +2   are NOT exactly consecutive integers......they are either consecutive ODD or EVEN integers

x and x+1 are consecutive integers     so I am not sure what your question means.....but if it is supposed to be x and x+1 then:

1/x   +  1/(x+1) = 29/420   multiply both sides by x(x+1)

x+1  + x  = 29/240 ( x^2 + x)       now solve for 'x'                                then the other number is x+1

If your Q IS supposed to be x and x+2 then

1/x + 1/(x+2) = 29/240     multiply both sides by x(x+2)

x+2    + x    = 29 / 240 ( x^2 + 2x)       solve for x                               then the other number is  x+2

Can you finish?

Jul 23, 2021

#1
+36430
+2

x and x +2   are NOT exactly consecutive integers......they are either consecutive ODD or EVEN integers

x and x+1 are consecutive integers     so I am not sure what your question means.....but if it is supposed to be x and x+1 then:

1/x   +  1/(x+1) = 29/420   multiply both sides by x(x+1)

x+1  + x  = 29/240 ( x^2 + x)       now solve for 'x'                                then the other number is x+1

If your Q IS supposed to be x and x+2 then

1/x + 1/(x+2) = 29/240     multiply both sides by x(x+2)

x+2    + x    = 29 / 240 ( x^2 + 2x)       solve for x                               then the other number is  x+2

Can you finish?

ElectricPavlov Jul 23, 2021