Solve y=x^2-sqrt{12}x+3

$$y = x ^ { 2 } - \sqrt { 12 } x + 3$$

Solve for y

$$y=\left(x-\sqrt{3}\right)^{2}$$

Solution Steps

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$y=x^{2}-2\sqrt{3}x+3$$

Solve for x (complex solution)

$$x=\sqrt{y}+\sqrt{3}$$

$$x=-\sqrt{y}+\sqrt{3}$$

Solve for x

$$x=\sqrt{y}+\sqrt{3}$$

$$x=-\sqrt{y}+\sqrt{3}\text{, }y\geq 0$$