Réitigh {l}{(sqrt{2}-1)^2+(2sqrt{2}-1)^2}{+2sqrt{2}}

$$\left. \begin{array} { l } { ( \sqrt { 2 } - 1 ) ^ { 2 } + ( 2 \sqrt { 2 } - 1 ) ^ { 2 } } \\ { + 2 \sqrt { 2 } } \end{array} \right.$$

Luacháil

$$12-4\sqrt{2}\approx 6.343145751$$

Céimeanna Réitigh

Úsáid an teoirim dhéthéarmach \left(a-b\right)^{2}=a^{2}-2ab+b^{2} chun \left(\sqrt{2}-1\right)^{2} a leathnú.

$$\left(\sqrt{2}\right)^{2}-2\sqrt{2}+1+\left(2\sqrt{2}-1\right)^{2}+2\sqrt{2}$$

Is é 2 uimhir chearnach \sqrt{2}.

$$2-2\sqrt{2}+1+\left(2\sqrt{2}-1\right)^{2}+2\sqrt{2}$$

Suimigh 2 agus 1 chun 3 a fháil.

$$3-2\sqrt{2}+\left(2\sqrt{2}-1\right)^{2}+2\sqrt{2}$$

Úsáid an teoirim dhéthéarmach \left(a-b\right)^{2}=a^{2}-2ab+b^{2} chun \left(2\sqrt{2}-1\right)^{2} a leathnú.

$$3-2\sqrt{2}+4\left(\sqrt{2}\right)^{2}-4\sqrt{2}+1+2\sqrt{2}$$

Is é 2 uimhir chearnach \sqrt{2}.

$$3-2\sqrt{2}+4\times 2-4\sqrt{2}+1+2\sqrt{2}$$

Méadaigh 4 agus 2 chun 8 a fháil.

$$3-2\sqrt{2}+8-4\sqrt{2}+1+2\sqrt{2}$$

Suimigh 8 agus 1 chun 9 a fháil.

$$3-2\sqrt{2}+9-4\sqrt{2}+2\sqrt{2}$$

Suimigh 3 agus 9 chun 12 a fháil.

$$12-2\sqrt{2}-4\sqrt{2}+2\sqrt{2}$$

Comhcheangail -2\sqrt{2} agus -4\sqrt{2} chun -6\sqrt{2} a fháil.

$$12-6\sqrt{2}+2\sqrt{2}$$

Comhcheangail -6\sqrt{2} agus 2\sqrt{2} chun -4\sqrt{2} a fháil.

$$12-4\sqrt{2}$$