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Popular >

x^2-x-1>0

Solution

x^{2} - x - 1 > 0

Solution

x < \frac{- 5 + 1}{2} or x > \frac{5 + 1}{2}

+2

Interval Notation

(- \infty, \frac{- 5 + 1}{2}) \cup (\frac{5 + 1}{2}, \infty)

Decimal Notation

x < - 0.61803 \dots or x > 1.61803 \dots

Solution steps

x^{2} - x - 1 > 0

Complete the square

x^{2} - x - 1 : (x - \frac{1}{2})^{2} - \frac{5}{4}

(x - \frac{1}{2})^{2} - \frac{5}{4} > 0

Move

\frac{5}{4}

to the right side

(x - \frac{1}{2})^{2} > \frac{5}{4}

For

u^{n} > a

, if

n

is even then

x - \frac{1}{2} < - \frac{5}{4} or x - \frac{1}{2} > \frac{5}{4}

x - \frac{1}{2} < - \frac{5}{4} : x < \frac{- 5 + 1}{2}

x - \frac{1}{2} > \frac{5}{4} : x > \frac{5 + 1}{2}

Combine the intervals

x < \frac{- 5 + 1}{2} or x > \frac{5 + 1}{2}

Popular Examples

5 u - 9 = - 7 u - 9

simplify (-21w^5x^2)/(7w^4x^5)simplify

\frac{- 21 w ^{5} x ^{2}}{7 w ^{4} x ^{5}}

x^{2} - 9 x + 14 \leq 0

simplify i^{72}simplify

i^{72}

m + (- 12) = - 8

Frequently Asked Questions (FAQ)

What is x^2-x-1>0 ?
The solution to x^2-x-1>0 is x<(-sqrt(5)+1)/2 \lor x>(sqrt(5)+1)/2