Question 151173
The sum of the reciprocals of two consecutive odd integers is 16 times the reciprocal of their products. Find these integer.
:
Two consecutive odd integers: x, (x+2)
:
write an equation for following statement
"The sum of the reciprocals of two consecutive odd integers is 16 times the reciprocal of their product."
{{{1/x}}} + {{{1/((x+2))}}} = 16({{{1/(x(x+2))}}})
:
{{{1/x}}} + {{{1/((x+2))}}} = {{{16/(x(x+2))}}}
Multiply equation by x(x+2)
:
(x+2) + x = 16
;
2x = 16 - 2
x = {{{14/2}}}
x = 7 & 9 are the two consecutive odd integers
;
:
Check solution in original equation:
{{{1/7}}} + {{{1/9}}} = 16({{{1/(7*9)}}})
{{{1/7}}} + {{{1/9}}} = {{{16/63}}}
{{{9/63}}} + {{{7/63}}} = {{{16/63}}}