Final answer:
The equation x´-3x²+2=0 can be solved using substitution by setting u = x², resulting in a quadratic equation. Solving the quadratic gives u = 2 or u = 1. Substituting back to x², we find four solutions for x: ±√2 and ±1.
Step-by-step explanation:
To solve the equation x´-3x²+2=0 using substitution, we'll let u = x². Now, the equation becomes a quadratic in terms of u: u²-3u+2=0. This can be solved by factoring, the quadratic formula, or by completing the square. Factoring, we find (u-2)(u-1)=0, which gives us u=2 or u=1.
Next, we substitute back for x to find the original variable's values. Substituting u=2 into u=x², we get x²=2; solving for x gives x=±√2. Similarly, substituting u=1 into u=x², we get x²=1; solving for x gives x=±1. So the original equation has four real solutions: ±√2 and ±1.