x^2-x+1>0

Solution

x^{2} - x + 1 > 0

True for all x

Interval Notation

(- \infty, \infty)

Solution steps

x^{2} - x + 1 > 0

Complete the square

x^{2} - x + 1 : (x - \frac{1}{2})^{2} + \frac{3}{4}

(x - \frac{1}{2})^{2} + \frac{3}{4} > 0

Move

\frac{3}{4}

to the right side

(x - \frac{1}{2})^{2} > - \frac{3}{4}

If n is even,

u^{n} \geq 0

for all

u

True for all x

x^{4} - 14 x^{3} + 71 x^{2} - 154 x + 120

409 6^{\frac{1}{4}}

- 108 - - 3

a b

2 - 5 (x + 5) = 3 (x - 2) - 1