Réitigh frac{sqrt{2}}{2}2+1/sqrt{3}=3x^2+15/sqrt{3}

Réitigh do x. (complex solution)

Graf

Tráth na gCeist

Algebra

5 fadhbanna cosúil le:

Fadhbanna den chineál céanna ó Chuardach Gréasáin

https://math.stackexchange.com/questions/1878973/real-function-with-complex-antiderivative-frac-sqrtx-sqrtx21-sqrtx

https://math.stackexchange.com/questions/730198/show-fx-sqrtx41-sqrtx4x2-rightarrow-1-2-for-x-rightarrow-i

https://math.stackexchange.com/questions/1842720/whats-the-mistake-on-my-answer-for-this-inequality-frac-leftx1-right-s

Roinn

Cóipeáladh go dtí an ghearrthaisce

2\sqrt{2}+\frac{2}{3}\times 3^{\frac{1}{2}}=\frac{2}{3}\times 3^{\frac{1}{2}}\left(3x^{2}+15\right)

Méadaigh an dá thaobh den chothromóid faoi 2.

2\sqrt{2}+\frac{2}{3}\times 3^{\frac{1}{2}}=2\times 3^{\frac{1}{2}}x^{2}+10\times 3^{\frac{1}{2}}

Úsáid an t-airí dáileach chun \frac{2}{3}\times 3^{\frac{1}{2}} a mhéadú faoi 3x^{2}+15.

2\times 3^{\frac{1}{2}}x^{2}+10\times 3^{\frac{1}{2}}=2\sqrt{2}+\frac{2}{3}\times 3^{\frac{1}{2}}

Athraigh na taobhanna ionas go mbeidh na téarmaí inathraitheacha ar fad ar an taobh clé.

2\times 3^{\frac{1}{2}}x^{2}=2\sqrt{2}+\frac{2}{3}\times 3^{\frac{1}{2}}-10\times 3^{\frac{1}{2}}

Bain 10\times 3^{\frac{1}{2}} ón dá thaobh.

2\times 3^{\frac{1}{2}}x^{2}=2\sqrt{2}-\frac{28}{3}\times 3^{\frac{1}{2}}

Comhcheangail \frac{2}{3}\times 3^{\frac{1}{2}} agus -10\times 3^{\frac{1}{2}} chun -\frac{28}{3}\times 3^{\frac{1}{2}} a fháil.

2\sqrt{3}x^{2}=-\frac{28}{3}\sqrt{3}+2\sqrt{2}

Athordaigh na téarmaí.

x^{2}=\frac{-\frac{28\sqrt{3}}{3}+2\sqrt{2}}{2\sqrt{3}}

Má roinntear é faoi 2\sqrt{3} cuirtear an iolrúchán faoi 2\sqrt{3} ar ceal.

x^{2}=\frac{\sqrt{6}-14}{3}

Roinn -\frac{28\sqrt{3}}{3}+2\sqrt{2} faoi 2\sqrt{3}.

x=\frac{i\sqrt{42-3\sqrt{6}}}{3} x=-\frac{i\sqrt{42-3\sqrt{6}}}{3}

Tóg fréamh chearnach an dá thaobh den chothromóid.

2\sqrt{2}+\frac{2}{3}\times 3^{\frac{1}{2}}=\frac{2}{3}\times 3^{\frac{1}{2}}\left(3x^{2}+15\right)

Méadaigh an dá thaobh den chothromóid faoi 2.

2\sqrt{2}+\frac{2}{3}\times 3^{\frac{1}{2}}=2\times 3^{\frac{1}{2}}x^{2}+10\times 3^{\frac{1}{2}}

Úsáid an t-airí dáileach chun \frac{2}{3}\times 3^{\frac{1}{2}} a mhéadú faoi 3x^{2}+15.

2\times 3^{\frac{1}{2}}x^{2}+10\times 3^{\frac{1}{2}}=2\sqrt{2}+\frac{2}{3}\times 3^{\frac{1}{2}}

Athraigh na taobhanna ionas go mbeidh na téarmaí inathraitheacha ar fad ar an taobh clé.

2\times 3^{\frac{1}{2}}x^{2}+10\times 3^{\frac{1}{2}}-2\sqrt{2}=\frac{2}{3}\times 3^{\frac{1}{2}}

Bain 2\sqrt{2} ón dá thaobh.

2\times 3^{\frac{1}{2}}x^{2}+10\times 3^{\frac{1}{2}}-2\sqrt{2}-\frac{2}{3}\times 3^{\frac{1}{2}}=0

Bain \frac{2}{3}\times 3^{\frac{1}{2}} ón dá thaobh.

2\times 3^{\frac{1}{2}}x^{2}+\frac{28}{3}\times 3^{\frac{1}{2}}-2\sqrt{2}=0

Comhcheangail 10\times 3^{\frac{1}{2}} agus -\frac{2}{3}\times 3^{\frac{1}{2}} chun \frac{28}{3}\times 3^{\frac{1}{2}} a fháil.

2\sqrt{3}x^{2}-2\sqrt{2}+\frac{28}{3}\sqrt{3}=0

Athordaigh na téarmaí.

2\sqrt{3}x^{2}+\frac{28\sqrt{3}}{3}-2\sqrt{2}=0

Is féidir cothromóidí cearnacha cosúil leis an gceann seo, le téarma x^{2} ach gan téarma x, a réiteach fós ag baint úsáid as an bhfoirmle chearnach, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, nuair a chuirfear i bhfoirm chaighdeánach iad: ax^{2}+bx+c=0.

x=\frac{0±\sqrt{0^{2}-4\times 2\sqrt{3}\left(\frac{28\sqrt{3}}{3}-2\sqrt{2}\right)}}{2\times 2\sqrt{3}}

Tá an chothromóid seo i bhfoirm chaighdeánach: ax^{2}+bx+c=0. Cuir 2\sqrt{3} in ionad a, 0 in ionad b, agus -2\sqrt{2}+\frac{28\sqrt{3}}{3} in ionad c san fhoirmle chearnach, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

x=\frac{0±\sqrt{-4\times 2\sqrt{3}\left(\frac{28\sqrt{3}}{3}-2\sqrt{2}\right)}}{2\times 2\sqrt{3}}

Cearnóg 0.

x=\frac{0±\sqrt{\left(-8\sqrt{3}\right)\left(\frac{28\sqrt{3}}{3}-2\sqrt{2}\right)}}{2\times 2\sqrt{3}}

Méadaigh -4 faoi 2\sqrt{3}.

x=\frac{0±\sqrt{16\sqrt{6}-224}}{2\times 2\sqrt{3}}

Méadaigh -8\sqrt{3} faoi -2\sqrt{2}+\frac{28\sqrt{3}}{3}.

x=\frac{0±4i\sqrt{14-\sqrt{6}}}{2\times 2\sqrt{3}}

Tóg fréamh chearnach 16\sqrt{6}-224.

x=\frac{0±4i\sqrt{14-\sqrt{6}}}{4\sqrt{3}}

Méadaigh 2 faoi 2\sqrt{3}.

x=\frac{i\sqrt{42-3\sqrt{6}}}{3}

Réitigh an chothromóid x=\frac{0±4i\sqrt{14-\sqrt{6}}}{4\sqrt{3}} nuair is ionann ± agus plus.