x/x^2 = 11 x/11x^2 = 1 x = 11x^2 11x^2 - x = 0 11x^2 - x - 0 = 0 (1+or-sqrt(1 - 4*11*0))/22 = x (1+or-1)/22 = x x = 2/22 or 0/22 x = 1/11 or 0, Some may regard 0 as an extraneous or undefined answer as it is saying 0/0 = 0. Quadratic formula can sometimes be used even when a coefficient is 0.
My math teacher definitely would fail the first solution: you have quadratic equation, but simply solve it by dividing by x without telling why we are allowed to do it. after all 11xx-x = x(11x - 1) = 0, so x=0 is the solution to the equation. From original equation follows that x > 0 (we have sqrt that requires positive and div x which requires x != 0)
x/x^2 = 11
x/11x^2 = 1
x = 11x^2
11x^2 - x = 0
11x^2 - x - 0 = 0
(1+or-sqrt(1 - 4*11*0))/22 = x
(1+or-1)/22 = x
x = 2/22 or 0/22
x = 1/11 or 0,
Some may regard 0 as an extraneous or undefined answer as it is saying 0/0 = 0.
Quadratic formula can sometimes be used even when a coefficient is 0.
My math teacher definitely would fail the first solution: you have quadratic equation, but simply solve it by dividing by x without telling why we are allowed to do it.
after all 11xx-x = x(11x - 1) = 0, so x=0 is the solution to the equation. From original equation follows that x > 0 (we have sqrt that requires positive and div x which requires x != 0)
Why do you not factor x into sqrt(x)*sqrt(x)
My friend....looking at you detailing 1/2-1 = 1/2-1/1 really bores me to death.....