What is sqrt(x^2-1)-3>2 ?

The solution to sqrt(x^2-1)-3>2 is x sqrt(26)

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sqrt(x^2-1)-3>2

x^{2} - 1 - 3 > 2

x < - 26 or x > 26

Interval Notation

(- \infty, - 26) \cup (26, \infty)

Decimal Notation

x < - 5.09901 \dots or x > 5.09901 \dots

Solution steps

x^{2} - 1 - 3 > 2

Move

3

to the right side

x^{2} - 1 > 5

Square both sides

(x^{2} - 1)^{2} > 5^{2}

Simplify

x^{2} - 1 > 25

x^{2} - 1 > 25 : x < - 26 or x > 26

x < - 26 or x > 26

Find singularity points

Find non-negative values for radicals:

x \leq - 1 or x \geq 1

Combine the intervals

(x < - 26 or x > 26) and (x \leq - 1 or x \geq 1)

Merge Overlapping Intervals

x < - 26 or x > 26

- 5 x + 13 \geq - 7

- 5 \leq 3 x - 2 < 7

9 n^{2} - 23 n + 20 = 3 n^{2}

x^{3} - 6 x^{2} + 5 x + 12

4 (2 x - 3) - 2 (3 x - 1) = - 14

What is sqrt(x^2-1)-3>2 ?
The solution to sqrt(x^2-1)-3>2 is x<-sqrt(26)\lor x>sqrt(26)