Réitigh (sqrt{5}-sqrt{3})(sqrt{5}+sqrt{3})-(sqrt{6}+sqrt{2})^2

$$( \sqrt { 5 } - \sqrt { 3 } ) ( \sqrt { 5 } + \sqrt { 3 } ) - ( \sqrt { 6 } + \sqrt { 2 } ) ^ { 2 }$$

Luacháil

$$-4\sqrt{3}-6\approx -12.92820323$$

Céimeanna Réitigh

Mar shampla \left(\sqrt{5}-\sqrt{3}\right)\left(\sqrt{5}+\sqrt{3}\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}.

$$\left(\sqrt{5}\right)^{2}-\left(\sqrt{3}\right)^{2}-\left(\sqrt{6}+\sqrt{2}\right)^{2}$$

Is é 5 uimhir chearnach \sqrt{5}.

$$5-\left(\sqrt{3}\right)^{2}-\left(\sqrt{6}+\sqrt{2}\right)^{2}$$

Is é 3 uimhir chearnach \sqrt{3}.

$$5-3-\left(\sqrt{6}+\sqrt{2}\right)^{2}$$

Dealaigh 3 ó 5 chun 2 a fháil.

$$2-\left(\sqrt{6}+\sqrt{2}\right)^{2}$$

Úsáid an teoirim dhéthéarmach \left(a+b\right)^{2}=a^{2}+2ab+b^{2} chun \left(\sqrt{6}+\sqrt{2}\right)^{2} a leathnú.

$$2-\left(\left(\sqrt{6}\right)^{2}+2\sqrt{6}\sqrt{2}+\left(\sqrt{2}\right)^{2}\right)$$

Is é 6 uimhir chearnach \sqrt{6}.

$$2-\left(6+2\sqrt{6}\sqrt{2}+\left(\sqrt{2}\right)^{2}\right)$$

Fachtóirigh 6=2\times 3. Athscríobh fréamh cearnach an toraidh \sqrt{2\times 3} mar thoradh na bhfréamhacha cearnacha \sqrt{2}\sqrt{3}.

$$2-\left(6+2\sqrt{2}\sqrt{3}\sqrt{2}+\left(\sqrt{2}\right)^{2}\right)$$

Méadaigh \sqrt{2} agus \sqrt{2} chun 2 a fháil.

$$2-\left(6+2\times 2\sqrt{3}+\left(\sqrt{2}\right)^{2}\right)$$

Méadaigh 2 agus 2 chun 4 a fháil.

$$2-\left(6+4\sqrt{3}+\left(\sqrt{2}\right)^{2}\right)$$

Is é 2 uimhir chearnach \sqrt{2}.

$$2-\left(6+4\sqrt{3}+2\right)$$

Suimigh 6 agus 2 chun 8 a fháil.

$$2-\left(8+4\sqrt{3}\right)$$

Chun an mhalairt ar 8+4\sqrt{3} a aimsiú, aimsigh an mhalairt ar gach téarma.

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

Dealaigh 8 ó 2 chun -6 a fháil.

$$-6-4\sqrt{3}$$