What is x^4-12x^2+40>= x^2+4 ?

The solution to x^4-12x^2+40>= x^2+4 is x = 3

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x^4-12x^2+40>= x^2+4

x^{4} - 12 x^{2} + 40 \geq x^{2} + 4

x \leq - 3 or - 2 \leq x \leq 2 or x \geq 3

Interval Notation

(- \infty, - 3] \cup [- 2, 2] \cup [3, \infty)

Solution steps

x^{4} - 12 x^{2} + 40 \geq x^{2} + 4

Rewrite in standard form

x^{4} - 13 x^{2} + 36 \geq 0

Factor

x^{4} - 13 x^{2} + 36 : (x + 2) (x - 2) (x + 3) (x - 3)

(x + 2) (x - 2) (x + 3) (x - 3) \geq 0

Identify the intervals

x \leq - 3 or - 2 \leq x \leq 2 or x \geq 3

10 x^{2} + 50 x

3 - (2 x - 5) < - 4 (x + 2)

3 x^{2} + 28 x + 9

v^{2} - 81

2 - \frac{x}{15} = - 3

What is x^4-12x^2+40>= x^2+4 ?
The solution to x^4-12x^2+40>= x^2+4 is x<=-3\lor-2<= x<= 2\lor x>= 3