Réitigh (a+bsqrt{2})*(1+sqrt{2})=25+17sqrt{2}

$$( a + b \sqrt { 2 } ) \cdot ( 1 + \sqrt { 2 } ) = 25 + 17 \sqrt { 2 }$$

Réitigh do a.

$$a=-\sqrt{2}\left(b-8\right)+9$$

Céimeanna chun Cothromóidí Líneacha a Réiteach

Úsáid an t-airí dáileach chun a+b\sqrt{2} a mhéadú faoi 1+\sqrt{2}.

$$a+a\sqrt{2}+b\sqrt{2}+b\left(\sqrt{2}\right)^{2}=25+17\sqrt{2}$$

Is é 2 uimhir chearnach \sqrt{2}.

$$a+a\sqrt{2}+b\sqrt{2}+b\times 2=25+17\sqrt{2}$$

Bain b\sqrt{2} ón dá thaobh.

$$a+a\sqrt{2}+b\times 2=25+17\sqrt{2}-b\sqrt{2}$$

Bain b\times 2 ón dá thaobh.

$$a+a\sqrt{2}=25+17\sqrt{2}-b\sqrt{2}-b\times 2$$

Méadaigh -1 agus 2 chun -2 a fháil.

$$a+a\sqrt{2}=25+17\sqrt{2}-b\sqrt{2}-2b$$

Comhcheangail na téarmaí ar fad ina bhfuil a.

$$\left(1+\sqrt{2}\right)a=25+17\sqrt{2}-b\sqrt{2}-2b$$

Tá an chothromóid i bhfoirm chaighdeánach.

$$\left(\sqrt{2}+1\right)a=-\sqrt{2}b-2b+17\sqrt{2}+25$$

Roinn an dá thaobh faoi 1+\sqrt{2}.

$$\frac{\left(\sqrt{2}+1\right)a}{\sqrt{2}+1}=\frac{-\sqrt{2}b-2b+17\sqrt{2}+25}{\sqrt{2}+1}$$

Má roinntear é faoi 1+\sqrt{2} cuirtear an iolrúchán faoi 1+\sqrt{2} ar ceal.

$$a=\frac{-\sqrt{2}b-2b+17\sqrt{2}+25}{\sqrt{2}+1}$$

Roinn 25+17\sqrt{2}-b\sqrt{2}-2b faoi 1+\sqrt{2}.

$$a=-\sqrt{2}b+8\sqrt{2}+9$$

Réitigh do b.

$$b=-\frac{\sqrt{2}\left(a-8\sqrt{2}-9\right)}{2}$$

Céimeanna chun Cothromóidí Líneacha a Réiteach

Úsáid an t-airí dáileach chun a+b\sqrt{2} a mhéadú faoi 1+\sqrt{2}.

$$a+a\sqrt{2}+b\sqrt{2}+b\left(\sqrt{2}\right)^{2}=25+17\sqrt{2}$$

Is é 2 uimhir chearnach \sqrt{2}.

$$a+a\sqrt{2}+b\sqrt{2}+b\times 2=25+17\sqrt{2}$$

Bain a ón dá thaobh.

$$a\sqrt{2}+b\sqrt{2}+b\times 2=25+17\sqrt{2}-a$$

Bain a\sqrt{2} ón dá thaobh.

$$b\sqrt{2}+b\times 2=25+17\sqrt{2}-a-a\sqrt{2}$$

Athordaigh na téarmaí.

$$\sqrt{2}b+2b=-\sqrt{2}a-a+17\sqrt{2}+25$$

Comhcheangail na téarmaí ar fad ina bhfuil b.

$$\left(\sqrt{2}+2\right)b=-\sqrt{2}a-a+17\sqrt{2}+25$$

Roinn an dá thaobh faoi \sqrt{2}+2.

$$\frac{\left(\sqrt{2}+2\right)b}{\sqrt{2}+2}=\frac{-\sqrt{2}a-a+17\sqrt{2}+25}{\sqrt{2}+2}$$

Má roinntear é faoi \sqrt{2}+2 cuirtear an iolrúchán faoi \sqrt{2}+2 ar ceal.

$$b=\frac{-\sqrt{2}a-a+17\sqrt{2}+25}{\sqrt{2}+2}$$

Roinn -\sqrt{2}a-a+17\sqrt{2}+25 faoi \sqrt{2}+2.

$$b=\frac{\left(2-\sqrt{2}\right)\left(-\sqrt{2}a-a+17\sqrt{2}+25\right)}{2}$$