What is 2x^2-x^4>= 0 ?

The solution to 2x^2-x^4>= 0 is -sqrt(2)<= x<= sqrt(2)

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2x^2-x^4>= 0

2 x^{2} - x^{4} \geq 0

- 2 \leq x \leq 2

Interval Notation

[- 2, 2]

Decimal Notation

- 1.41421 \dots \leq x \leq 1.41421 \dots

Solution steps

2 x^{2} - x^{4} \geq 0

Factor

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

- x^{2} (x + 2) (x - 2) \geq 0

Multiply both sides by

- 1

(reverse the inequality)

(- x^{2} (x + 2) (x - 2)) (- 1) \leq 0 \cdot (- 1)

Simplify

x^{2} (x + 2) (x - 2) \leq 0

Identify the intervals

- 2 \leq x \leq 2

x + x + 2 = 68

\frac{3}{4} (x - 7) \geq x + 2

\frac{1}{9}

8 > - 2 x + 4 > - 2

- x^{2} - x + 3 = 0