Réitigh 2/sqrt{2-2}+frac{sqrt{2}+1}{sqrt{2}-1}-frac{sqrt{32}}{2}

$$\frac { 2 } { \sqrt { 2 } - 2 } + \frac { \sqrt { 2 } + 1 } { \sqrt { 2 } - 1 } - \frac { \sqrt { 32 } } { 2 }$$

Luacháil

$$1-\sqrt{2}\approx -0.414213562$$

Céimeanna Réitigh

Iolraigh an t-uimhreoir agus an t-ainmneoir faoi \sqrt{2}+2 chun ainmneoir \frac{2}{\sqrt{2}-2} a thiontú in uimhir chóimheasta.

$$\frac{2\left(\sqrt{2}+2\right)}{\left(\sqrt{2}-2\right)\left(\sqrt{2}+2\right)}+\frac{\sqrt{2}+1}{\sqrt{2}-1}-\frac{\sqrt{32}}{2}$$

Mar shampla \left(\sqrt{2}-2\right)\left(\sqrt{2}+2\right). Is féidir iolrúchán a athrú ó bhonn go dtí difríocht na gcearnóg ag úsáid na rialach seo: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{2\left(\sqrt{2}+2\right)}{\left(\sqrt{2}\right)^{2}-2^{2}}+\frac{\sqrt{2}+1}{\sqrt{2}-1}-\frac{\sqrt{32}}{2}$$

Cearnóg \sqrt{2}. Cearnóg 2.

$$\frac{2\left(\sqrt{2}+2\right)}{2-4}+\frac{\sqrt{2}+1}{\sqrt{2}-1}-\frac{\sqrt{32}}{2}$$

Dealaigh 4 ó 2 chun -2 a fháil.

$$\frac{2\left(\sqrt{2}+2\right)}{-2}+\frac{\sqrt{2}+1}{\sqrt{2}-1}-\frac{\sqrt{32}}{2}$$

Cealaigh -2 agus -2.

$$-\left(\sqrt{2}+2\right)+\frac{\sqrt{2}+1}{\sqrt{2}-1}-\frac{\sqrt{32}}{2}$$

Iolraigh an t-uimhreoir agus an t-ainmneoir faoi \sqrt{2}+1 chun ainmneoir \frac{\sqrt{2}+1}{\sqrt{2}-1} a thiontú in uimhir chóimheasta.

$$-\left(\sqrt{2}+2\right)+\frac{\left(\sqrt{2}+1\right)\left(\sqrt{2}+1\right)}{\left(\sqrt{2}-1\right)\left(\sqrt{2}+1\right)}-\frac{\sqrt{32}}{2}$$

Mar shampla \left(\sqrt{2}-1\right)\left(\sqrt{2}+1\right). Is féidir iolrúchán a athrú ó bhonn go dtí difríocht na gcearnóg ag úsáid na rialach seo: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$-\left(\sqrt{2}+2\right)+\frac{\left(\sqrt{2}+1\right)\left(\sqrt{2}+1\right)}{\left(\sqrt{2}\right)^{2}-1^{2}}-\frac{\sqrt{32}}{2}$$

Cearnóg \sqrt{2}. Cearnóg 1.

$$-\left(\sqrt{2}+2\right)+\frac{\left(\sqrt{2}+1\right)\left(\sqrt{2}+1\right)}{2-1}-\frac{\sqrt{32}}{2}$$

Dealaigh 1 ó 2 chun 1 a fháil.

$$-\left(\sqrt{2}+2\right)+\frac{\left(\sqrt{2}+1\right)\left(\sqrt{2}+1\right)}{1}-\frac{\sqrt{32}}{2}$$

Tugann aon rud a roinntear ar a haon é féin.

$$-\left(\sqrt{2}+2\right)+\left(\sqrt{2}+1\right)\left(\sqrt{2}+1\right)-\frac{\sqrt{32}}{2}$$

Méadaigh \sqrt{2}+1 agus \sqrt{2}+1 chun \left(\sqrt{2}+1\right)^{2} a fháil.

$$-\left(\sqrt{2}+2\right)+\left(\sqrt{2}+1\right)^{2}-\frac{\sqrt{32}}{2}$$

Fachtóirigh 32=4^{2}\times 2. Athscríobh fréamh cearnach an toraidh \sqrt{4^{2}\times 2} mar thoradh na bhfréamhacha cearnacha \sqrt{4^{2}}\sqrt{2}. Tóg fréamh chearnach 4^{2}.

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

Roinn 4\sqrt{2} faoi 2 chun 2\sqrt{2} a fháil.

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

Chun an mhalairt ar \sqrt{2}+2 a aimsiú, aimsigh an mhalairt ar gach téarma.

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

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

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

Is é 2 uimhir chearnach \sqrt{2}.

$$-\sqrt{2}-2+2+2\sqrt{2}+1-2\sqrt{2}$$

Suimigh 2 agus 1 chun 3 a fháil.

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

Suimigh -2 agus 3 chun 1 a fháil.

$$-\sqrt{2}+1+2\sqrt{2}-2\sqrt{2}$$

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

$$\sqrt{2}+1-2\sqrt{2}$$

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

$$-\sqrt{2}+1$$

Fachtóirigh

$$1-\sqrt{2}$$