What is (x+1+sqrt(5))^2+5>= 3-(x+1+sqrt(3))^2 ?

The solution to (x+1+sqrt(5))^2+5>= 3-(x+1+sqrt(3))^2 is True for all x

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(x+1+sqrt(5))^2+5>= 3-(x+1+sqrt(3))^2

(x + 1 + 5)^{2} + 5 \geq 3 - (x + 1 + 3)^{2}

True for all x

Interval Notation

(- \infty, \infty)

Solution steps

(x + 1 + 5)^{2} + 5 \geq 3 - (x + 1 + 3)^{2}

Rewrite in standard form

2 x^{2} + 4 x + 25 x + 23 x + 12 + 25 + 23 \geq 0

Factor

2 x^{2} + 4 x + 25 x + 23 x + 12 + 25 + 23 : 2 x^{2} + 4 x + 25 x + 23 x + 12 + 25 + 23 \geq 0

2 x^{2} + 4 x + 25 x + 23 x + 12 + 25 + 23 \geq 0

Identify the intervals

True for all x

\frac{3}{x} < 1

(- 3 x + 1) (- 3 x + 4) > - 2 x + 26

m^{2} < 16

2^{1} - x^{2} < 8

3 x (x - 2) < 0

What is (x+1+sqrt(5))^2+5>= 3-(x+1+sqrt(3))^2 ?
The solution to (x+1+sqrt(5))^2+5>= 3-(x+1+sqrt(3))^2 is True for all x