Solve k(k-k)^3-3(k-k)+1geq0

$$k ( k - k ) ^ { 3 } - 3 ( k - k ) + 1 \geq 0$$

Evaluate (complex solution)

Solution Steps

Combine k and -k to get 0.

$$k\times 0^{3}-3\left(k-k\right)+1\geq 0$$

Calculate 0 to the power of 3 and get 0.

$$k\times 0-3\left(k-k\right)+1\geq 0$$

Anything times zero gives zero.

$$0-3\left(k-k\right)+1\geq 0$$

Combine k and -k to get 0.

$$0-3\times 0+1\geq 0$$

Multiply 3 and 0 to get 0.

$$0-0+1\geq 0$$

Subtracting 0 from itself leaves 0.

$$0+1\geq 0$$

Add 0 and 1 to get 1.

$$1\geq 0$$

Compare 1 and 0.

$$\text{true}$$

Solve for k

$$k\in \mathrm{R}$$

Solution Steps

Combine k and -k to get 0.

$$k\times 0^{3}-3\left(k-k\right)+1\geq 0$$

Calculate 0 to the power of 3 and get 0.

$$k\times 0-3\left(k-k\right)+1\geq 0$$

Anything times zero gives zero.

$$0-3\left(k-k\right)+1\geq 0$$

Combine k and -k to get 0.

$$0-3\times 0+1\geq 0$$

Multiply 3 and 0 to get 0.

$$0-0+1\geq 0$$

Subtracting 0 from itself leaves 0.

$$0+1\geq 0$$

Add 0 and 1 to get 1.

$$1\geq 0$$

This is true for any k.

$$k\in \mathrm{R}$$