Nếu \(x < 1\) thì \(x^{8} - x^{7} + x^{2} - x + 1\)

\(= x^{8} + x^{2} \left(\right. 1 - x^{5} \left.\right) + \left(\right. 1 - x \left.\right) > 0\).

Nếu \(x \geq 1\) thì \(x^{8} - x^{7} + x^{2} - x + 1\)

\(= x^{7} \left(\right. x - 1 \left.\right) + x \left(\right. x - 1 \left.\right) + 1 > 0\).

Nếu \(x < 1\) thì \(x^{8} - x^{7} + x^{2} - x + 1\)

\(= x^{8} + x^{2} \left(\right. 1 - x^{5} \left.\right) + \left(\right. 1 - x \left.\right) > 0\).

Nếu \(x \geq 1\) thì \(x^{8} - x^{7} + x^{2} - x + 1\)

\(= x^{7} \left(\right. x - 1 \left.\right) + x \left(\right. x - 1 \left.\right) + 1 > 0\).

Nếu \(x < 1\) thì \(x^{8} - x^{7} + x^{2} - x + 1\)

\(= x^{8} + x^{2} \left(\right. 1 - x^{5} \left.\right) + \left(\right. 1 - x \left.\right) > 0\).

Nếu \(x \geq 1\) thì \(x^{8} - x^{7} + x^{2} - x + 1\)

\(= x^{7} \left(\right. x - 1 \left.\right) + x \left(\right. x - 1 \left.\right) + 1 > 0\).

Nếu \(x < 1\) thì \(x^{8} - x^{7} + x^{2} - x + 1\)

\(= x^{8} + x^{2} \left(\right. 1 - x^{5} \left.\right) + \left(\right. 1 - x \left.\right) > 0\).

Nếu \(x \geq 1\) thì \(x^{8} - x^{7} + x^{2} - x + 1\)

\(= x^{7} \left(\right. x - 1 \left.\right) + x \left(\right. x - 1 \left.\right) + 1 > 0\).

Nếu \(x < 1\) thì \(x^{8} - x^{7} + x^{2} - x + 1\)

\(= x^{8} + x^{2} \left(\right. 1 - x^{5} \left.\right) + \left(\right. 1 - x \left.\right) > 0\).

Nếu \(x \geq 1\) thì \(x^{8} - x^{7} + x^{2} - x + 1\)

\(= x^{7} \left(\right. x - 1 \left.\right) + x \left(\right. x - 1 \left.\right) + 1 > 0\).

Nếu \(x < 1\) thì \(x^{8} - x^{7} + x^{2} - x + 1\)

\(= x^{8} + x^{2} \left(\right. 1 - x^{5} \left.\right) + \left(\right. 1 - x \left.\right) > 0\).

Nếu \(x \geq 1\) thì \(x^{8} - x^{7} + x^{2} - x + 1\)

\(= x^{7} \left(\right. x - 1 \left.\right) + x \left(\right. x - 1 \left.\right) + 1 > 0\).

Nếu \(x < 1\) thì \(x^{8} - x^{7} + x^{2} - x + 1\)

\(= x^{8} + x^{2} \left(\right. 1 - x^{5} \left.\right) + \left(\right. 1 - x \left.\right) > 0\).

Nếu \(x \geq 1\) thì \(x^{8} - x^{7} + x^{2} - x + 1\)

\(= x^{7} \left(\right. x - 1 \left.\right) + x \left(\right. x - 1 \left.\right) + 1 > 0\).

Nếu \(x < 1\) thì \(x^{8} - x^{7} + x^{2} - x + 1\)

\(= x^{8} + x^{2} \left(\right. 1 - x^{5} \left.\right) + \left(\right. 1 - x \left.\right) > 0\).

Nếu \(x \geq 1\) thì \(x^{8} - x^{7} + x^{2} - x + 1\)

\(= x^{7} \left(\right. x - 1 \left.\right) + x \left(\right. x - 1 \left.\right) + 1 > 0\).

Nếu \(x < 1\) thì \(x^{8} - x^{7} + x^{2} - x + 1\)

\(= x^{8} + x^{2} \left(\right. 1 - x^{5} \left.\right) + \left(\right. 1 - x \left.\right) > 0\).

Nếu \(x \geq 1\) thì \(x^{8} - x^{7} + x^{2} - x + 1\)

\(= x^{7} \left(\right. x - 1 \left.\right) + x \left(\right. x - 1 \left.\right) + 1 > 0\).

Nếu \(x < 1\) thì \(x^{8} - x^{7} + x^{2} - x + 1\)

\(= x^{8} + x^{2} \left(\right. 1 - x^{5} \left.\right) + \left(\right. 1 - x \left.\right) > 0\).

Nếu \(x \geq 1\) thì \(x^{8} - x^{7} + x^{2} - x + 1\)

\(= x^{7} \left(\right. x - 1 \left.\right) + x \left(\right. x - 1 \left.\right) + 1 > 0\).