Solve x^4-17x^2+4=0

$$x ^ { 4 } - 17 x ^ { 2 } + 4 = 0$$

Solve for x

$$x=\frac{\sqrt{13}-\sqrt{21}}{2}\approx -0.48851221$$

$$x=\frac{\sqrt{21}-\sqrt{13}}{2}\approx 0.48851221$$

$$x = \frac{\sqrt{13} + \sqrt{21}}{2} \approx 4.094063485$$

$$x=\frac{-\sqrt{13}-\sqrt{21}}{2}\approx -4.094063485$$

Steps Using the Quadratic Formula

Substitute t for x^{2}.

$$t^{2}-17t+4=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Substitute 1 for a, -17 for b, and 4 for c in the quadratic formula.

$$t=\frac{-\left(-17\right)±\sqrt{\left(-17\right)^{2}-4\times 1\times 4}}{2}$$

Do the calculations.

$$t=\frac{17±\sqrt{273}}{2}$$

Solve the equation t=\frac{17±\sqrt{273}}{2} when ± is plus and when ± is minus.

$$t=\frac{\sqrt{273}+17}{2} t=\frac{17-\sqrt{273}}{2}$$

Since x=t^{2}, the solutions are obtained by evaluating x=±\sqrt{t} for each t.

$$x=\frac{\sqrt{13}+\sqrt{21}}{2} x=-\frac{\sqrt{13}+\sqrt{21}}{2} x=-\frac{\sqrt{13}-\sqrt{21}}{2} x=\frac{\sqrt{13}-\sqrt{21}}{2}$$