Why is there no solution for the system of equations with a greater than 0?
Solve[{c^2 - b^4/a^2 == 0, a^2 + b^2 == c^2, e == c/a, a > 0,
e > 1}, e, {a, c}]
Why can we solve the value of e by setting a not equal to 0?
Solve[{c^2 - b^4/a^2 == 0, a^2 + b^2 == c^2, e == c/a, a != 0,
e > 1}, e, {a, c}]
{{e -> 1/2 (1 + Sqrt[5])}}
How can we solve this equation if a is greater than 0?
Solve[{(((2 Sqrt[2] + 2) a)^2 + 8 a^2 - 4 c^2)/(
2 (2 Sqrt[2] + 2) a 2 Sqrt[2] a) == Sqrt[2]/2, e == c/a, a > 0,
e > 1}, e, {a, c}]
the result is:
{{e -> Sqrt[3]}}
Solve[{c^2 - b^4/a^2 == 0, a^2 + b^2 == c^2, e == c/a, a > 0, e > 1}, e, {a, c}, Reals]
$\endgroup$Solve[{c^2 - b^4/a^2 == 0, a^2 + b^2 == c^2, e == c/a, a > 0, e > 1}, e, {a, b}, Reals]
is more informative. $\endgroup$