let one integer be x, the consecutive even integer is x+2
reciprocals are [tex] \frac{1}{x} and \frac{1}{x+2} [/tex]
[tex] \frac{1}{x} + \frac{1}{x+2} [/tex] =[tex] \frac{7}{12} [/tex]
make the denominators the same:
[tex] \frac{x+2}{x(x+2)} [/tex] + [tex] \frac{x}{x(x+2)} [/tex] =[tex] \frac{7}{12} [/tex]
[tex] \frac{2x+2}{x(x+2)} = \frac{7}{12} [/tex]
12(2x+2)=7x(x+2)
24x+24=7x²+14x
7x²-10x-24=0
the result is not a whole number. Something is not right about this question.
