Réitigh (7+3sqrt{2})^2-(5-2sqrt{5})^2

$$( 7 + 3 \sqrt { 2 } ) ^ { 2 } - ( 5 - 2 \sqrt { 5 } ) ^ { 2 }$$

Luacháil

$$20\sqrt{5}+42\sqrt{2}+22\approx 126.11832917$$

Céimeanna Réitigh

Úsáid an teoirim dhéthéarmach \left(a+b\right)^{2}=a^{2}+2ab+b^{2} chun \left(7+3\sqrt{2}\right)^{2} a leathnú.

$$49+42\sqrt{2}+9\left(\sqrt{2}\right)^{2}-\left(5-2\sqrt{5}\right)^{2}$$

Is é 2 uimhir chearnach \sqrt{2}.

$$49+42\sqrt{2}+9\times 2-\left(5-2\sqrt{5}\right)^{2}$$

Méadaigh 9 agus 2 chun 18 a fháil.

$$49+42\sqrt{2}+18-\left(5-2\sqrt{5}\right)^{2}$$

Suimigh 49 agus 18 chun 67 a fháil.

$$67+42\sqrt{2}-\left(5-2\sqrt{5}\right)^{2}$$

Úsáid an teoirim dhéthéarmach \left(a-b\right)^{2}=a^{2}-2ab+b^{2} chun \left(5-2\sqrt{5}\right)^{2} a leathnú.

$$67+42\sqrt{2}-\left(25-20\sqrt{5}+4\left(\sqrt{5}\right)^{2}\right)$$

Is é 5 uimhir chearnach \sqrt{5}.

$$67+42\sqrt{2}-\left(25-20\sqrt{5}+4\times 5\right)$$

Méadaigh 4 agus 5 chun 20 a fháil.

$$67+42\sqrt{2}-\left(25-20\sqrt{5}+20\right)$$

Suimigh 25 agus 20 chun 45 a fháil.

$$67+42\sqrt{2}-\left(45-20\sqrt{5}\right)$$

Chun an mhalairt ar 45-20\sqrt{5} a aimsiú, aimsigh an mhalairt ar gach téarma.

$$67+42\sqrt{2}-45+20\sqrt{5}$$

Dealaigh 45 ó 67 chun 22 a fháil.

$$22+42\sqrt{2}+20\sqrt{5}$$

Fairsingigh

$$20 \sqrt{5} + 42 \sqrt{2} + 22 = 126.11832917$$

Céimeanna Réitigh

Úsáid an teoirim dhéthéarmach \left(a+b\right)^{2}=a^{2}+2ab+b^{2} chun \left(7+3\sqrt{2}\right)^{2} a leathnú.

$$49+42\sqrt{2}+9\left(\sqrt{2}\right)^{2}-\left(5-2\sqrt{5}\right)^{2}$$

Is é 2 uimhir chearnach \sqrt{2}.

$$49+42\sqrt{2}+9\times 2-\left(5-2\sqrt{5}\right)^{2}$$

Méadaigh 9 agus 2 chun 18 a fháil.

$$49+42\sqrt{2}+18-\left(5-2\sqrt{5}\right)^{2}$$

Suimigh 49 agus 18 chun 67 a fháil.

$$67+42\sqrt{2}-\left(5-2\sqrt{5}\right)^{2}$$

Úsáid an teoirim dhéthéarmach \left(a-b\right)^{2}=a^{2}-2ab+b^{2} chun \left(5-2\sqrt{5}\right)^{2} a leathnú.

$$67+42\sqrt{2}-\left(25-20\sqrt{5}+4\left(\sqrt{5}\right)^{2}\right)$$

Is é 5 uimhir chearnach \sqrt{5}.

$$67+42\sqrt{2}-\left(25-20\sqrt{5}+4\times 5\right)$$

Méadaigh 4 agus 5 chun 20 a fháil.

$$67+42\sqrt{2}-\left(25-20\sqrt{5}+20\right)$$

Suimigh 25 agus 20 chun 45 a fháil.

$$67+42\sqrt{2}-\left(45-20\sqrt{5}\right)$$

Chun an mhalairt ar 45-20\sqrt{5} a aimsiú, aimsigh an mhalairt ar gach téarma.

$$67+42\sqrt{2}-45+20\sqrt{5}$$

Dealaigh 45 ó 67 chun 22 a fháil.

$$22+42\sqrt{2}+20\sqrt{5}$$