Issolvi (x+1)^2-2(x+1)-1leq0

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

Solvi għal x

$$x\in \begin{bmatrix}-\sqrt{2},\sqrt{2}\end{bmatrix}$$

Passi tas-Soluzzjonijiet

Uża teorema binomjali \left(a+b\right)^{2}=a^{2}+2ab+b^{2} biex tespandi \left(x+1\right)^{2}.

$$x^{2}+2x+1-2\left(x+1\right)-1\leq 0$$

Uża l-propjetà distributtiva biex timmultiplika -2 b'x+1.

$$x^{2}+2x+1-2x-2-1\leq 0$$

Ikkombina 2x u -2x biex tikseb 0.

$$x^{2}+1-2-1\leq 0$$

Naqqas 2 minn 1 biex tikseb -1.

$$x^{2}-1-1\leq 0$$

Naqqas 1 minn -1 biex tikseb -2.

$$x^{2}-2\leq 0$$

Żid 2 maż-żewġ naħat.

$$x^{2}\leq 2$$

Ikkalkula l-għerq kwadrat ta' 2 u ikseb \sqrt{2}. Erġa' ikteb 2 bħala \left(\sqrt{2}\right)^{2}.

$$x^{2}\leq \left(\sqrt{2}\right)^{2}$$

L-inugwaljanza żżomm għal |x|\leq \sqrt{2}.

$$|x|\leq \sqrt{2}$$

Erġa' ikteb |x|\leq \sqrt{2} bħala x\in \left[-\sqrt{2},\sqrt{2}\right].

$$x\in \begin{bmatrix}-\sqrt{2},\sqrt{2}\end{bmatrix}$$