x^4/3-7x^2/3+12=0 implify into quadratic equation
First of all multiply by 3
x^4 - 7x^2 + 36 = 0
then
(x^2)^2 - 7(x^2) +36 = 0
um . . . how can it be in the form of ax^2 + bx + c = 0?
To simplify the given equation into a quadratic equation, we can make a substitution to change the variable from x^2/3 to a new variable, say y. Here's how you do it:
1. Let y = x^2/3.
By substituting y for x^2/3, the equation becomes:
y^2 - 7y + 12 = 0.
Now we have a quadratic equation in terms of y.
2. Factor the quadratic equation.
The equation is already in its simplest form, and it factors to:
(y - 3)(y - 4) = 0.
3. Substitute back the value for y.
Now that we have factored the quadratic equation, substitute back x^2/3 for y:
(x^2/3 - 3)(x^2/3 - 4) = 0.
4. Simplify the equation.
To simplify the equation further, we can multiply through by 3 to get rid of the denominators:
(x^2 - 9)(x^2 - 12) = 0.
Now the equation is simplified into a quadratic equation form.