Question
Describe the values of a,b,and c for which the solutions of axx+b=c are rational
Answers
Damon
x^2 = (c-b)/a ?
x = sqrt [(c-b)/a]
well, (c-b)/a better be positive and a square of some integer (which makes it positive anyway)
for example if (c-b)/a = 5
then x = sqrt 5
which is hard to express as a ratio of integers
and if (c-b)/a is -4
then we have 2 i and i, the square root of -1, is not a rational number
x = sqrt [(c-b)/a]
well, (c-b)/a better be positive and a square of some integer (which makes it positive anyway)
for example if (c-b)/a = 5
then x = sqrt 5
which is hard to express as a ratio of integers
and if (c-b)/a is -4
then we have 2 i and i, the square root of -1, is not a rational number