What is |x^2-2|<= 1 ?

The solution to |x^2-2|<= 1 is -sqrt(3)<= x<=-1\lor 1<= x<= sqrt(3)

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|x^2-2|<= 1

x^{2} - 2 \leq 1

- 3 \leq x \leq - 1 or 1 \leq x \leq 3

Interval Notation

[- 3, - 1] \cup [1, 3]

Decimal Notation

- 1.73205 \dots \leq x \leq - 1 or 1 \leq x \leq 1.73205 \dots

Solution steps

x^{2} - 2 \leq 1

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 1 \leq x^{2} - 2 \leq 1

x^{2} - 2 \geq - 1 and x^{2} - 2 \leq 1

(x \leq - 1 or x \geq 1) and - 3 \leq x \leq 3

Merge Overlapping Intervals

- 3 \leq x \leq - 1 or 1 \leq x \leq 3

x + 7 = 9

4 x^{2} - 2 x - 6

4 - (- 5)

i^{54}

\frac{1}{1 - 2.5}

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