Solve -a^6+4a^3=3

$$- a ^ { 6 } + 4 a ^ { 3 } = 3$$

Solve for a

$$a=1$$

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

Steps Using the Quadratic Formula

Subtract 3 from both sides.

$$-a^{6}+4a^{3}-3=0$$

Substitute t for a^{3}.

$$-t^{2}+4t-3=0$$

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

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

Do the calculations.

$$t=\frac{-4±2}{-2}$$

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

$$t=1 t=3$$

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

$$a=1 a=\sqrt[3]{3}$$