Question 371970

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Hi,
Let x represent the integer
question states
x + 1/x = 65/8    Multiplying each term by 8x so as all denominators = 1
8x^2 + 8 = 65x
8x^2 - 65x + 8 = 0
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{x = (65 +- sqrt( 3969 ))/(16) }}}
{{{x = (65 +- 63)/(16) }}}
x = 2/16  cannot use (not an integer)
x = 128/16
x = 8
checking our answer
8 + 1/8 = 64/8 + 1/8 = 65/8