The solution to x^2-4x+1<0 is -sqrt(3)+2<x<sqrt(3)+2

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x^2-4x+1<0

Solution

x^{2} - 4 x + 1 < 0

- 3 + 2 < x < 3 + 2

Interval Notation

(- 3 + 2, 3 + 2)

Decimal Notation

0.26794 \dots < x < 3.73205 \dots

Solution steps

x^{2} - 4 x + 1 < 0

Complete the square

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

(x - 2)^{2} - 3 < 0

Move

3

to the right side

(x - 2)^{2} < 3

For

u^{n} < a

, if

n

is even then

- 3 < x - 2 < 3

a < u < b

then

a < u and u < b

- 3 < x - 2 and x - 2 < 3

- 3 < x - 2 : x > - 3 + 2

x - 2 < 3 : x < 3 + 2

Combine the intervals

x > - 3 + 2 and x < 3 + 2

Merge Overlapping Intervals

- 3 + 2 < x < 3 + 2

x \cdot x^{- 2}

\frac{y - 1}{4} - \frac{2 y + 5}{3} = \frac{1}{6}

- 5 x^{2} + 2 x + 39 = 0

6 x^{2} + 23 x + 20

x (x + 4) \leq 0