Solve t^6-2t^3-3=0

$$t ^ { 6 } - 2 t ^ { 3 } - 3 = 0$$

Solve for t

$$t=-1$$

$$t=\sqrt[3]{3}\approx 1.44224957$$

Steps Using the Quadratic Formula

Substitute t for t^{3}.

$$t^{2}-2t-3=0$$

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, -2 for b, and -3 for c in the quadratic formula.

$$t=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\times 1\left(-3\right)}}{2}$$

Do the calculations.

$$t=\frac{2±4}{2}$$

Solve the equation t=\frac{2±4}{2} when ± is plus and when ± is minus.

$$t=3 t=-1$$

Since t=t^{3}, the solutions are obtained by evaluating t=\sqrt[3]{t} for each t.

$$t=\sqrt[3]{3} t=-1$$