Luacháil
\sqrt{5}\approx 2.236067977
Tráth na gCeist
Arithmetic
5 fadhbanna cosúil le:
\frac { 7 + 3 \sqrt { 5 } } { 3 + \sqrt { 5 } } - \frac { 7 - 3 \sqrt { 5 } } { 3 - \sqrt { 5 } }
Roinn
Cóipeáladh go dtí an ghearrthaisce
\frac{\left(7+3\sqrt{5}\right)\left(3-\sqrt{5}\right)}{\left(3+\sqrt{5}\right)\left(3-\sqrt{5}\right)}-\frac{7-3\sqrt{5}}{3-\sqrt{5}}
Iolraigh an t-uimhreoir agus an t-ainmneoir faoi 3-\sqrt{5} chun ainmneoir \frac{7+3\sqrt{5}}{3+\sqrt{5}} a thiontú in uimhir chóimheasta.
\frac{\left(7+3\sqrt{5}\right)\left(3-\sqrt{5}\right)}{3^{2}-\left(\sqrt{5}\right)^{2}}-\frac{7-3\sqrt{5}}{3-\sqrt{5}}
Mar shampla \left(3+\sqrt{5}\right)\left(3-\sqrt{5}\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{\left(7+3\sqrt{5}\right)\left(3-\sqrt{5}\right)}{9-5}-\frac{7-3\sqrt{5}}{3-\sqrt{5}}
Cearnóg 3. Cearnóg \sqrt{5}.
\frac{\left(7+3\sqrt{5}\right)\left(3-\sqrt{5}\right)}{4}-\frac{7-3\sqrt{5}}{3-\sqrt{5}}
Dealaigh 5 ó 9 chun 4 a fháil.
\frac{\left(7+3\sqrt{5}\right)\left(3-\sqrt{5}\right)}{4}-\frac{\left(7-3\sqrt{5}\right)\left(3+\sqrt{5}\right)}{\left(3-\sqrt{5}\right)\left(3+\sqrt{5}\right)}
Iolraigh an t-uimhreoir agus an t-ainmneoir faoi 3+\sqrt{5} chun ainmneoir \frac{7-3\sqrt{5}}{3-\sqrt{5}} a thiontú in uimhir chóimheasta.
\frac{\left(7+3\sqrt{5}\right)\left(3-\sqrt{5}\right)}{4}-\frac{\left(7-3\sqrt{5}\right)\left(3+\sqrt{5}\right)}{3^{2}-\left(\sqrt{5}\right)^{2}}
Mar shampla \left(3-\sqrt{5}\right)\left(3+\sqrt{5}\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{\left(7+3\sqrt{5}\right)\left(3-\sqrt{5}\right)}{4}-\frac{\left(7-3\sqrt{5}\right)\left(3+\sqrt{5}\right)}{9-5}
Cearnóg 3. Cearnóg \sqrt{5}.
\frac{\left(7+3\sqrt{5}\right)\left(3-\sqrt{5}\right)}{4}-\frac{\left(7-3\sqrt{5}\right)\left(3+\sqrt{5}\right)}{4}
Dealaigh 5 ó 9 chun 4 a fháil.
\frac{\left(7+3\sqrt{5}\right)\left(3-\sqrt{5}\right)-\left(7-3\sqrt{5}\right)\left(3+\sqrt{5}\right)}{4}
Tá an t-ainmneoir céanna ag \frac{\left(7+3\sqrt{5}\right)\left(3-\sqrt{5}\right)}{4} agus \frac{\left(7-3\sqrt{5}\right)\left(3+\sqrt{5}\right)}{4} agus, mar sin, is féidir iad a dhealú trína n-uimhreoirí a dhealú.
\frac{21-7\sqrt{5}+9\sqrt{5}-15-21-7\sqrt{5}+9\sqrt{5}+15}{4}
Déan iolrúcháin in \left(7+3\sqrt{5}\right)\left(3-\sqrt{5}\right)-\left(7-3\sqrt{5}\right)\left(3+\sqrt{5}\right).
\frac{4\sqrt{5}}{4}
Déan áirimh in 21-7\sqrt{5}+9\sqrt{5}-15-21-7\sqrt{5}+9\sqrt{5}+15.
\sqrt{5}
Cealaigh 4 agus 4.
Samplaí
Cothromóid chearnach
{ x } ^ { 2 } - 4 x - 5 = 0
Triantánacht
4 \sin \theta \cos \theta = 2 \sin \theta
Cothromóid líneach
y = 3x + 4
Uimhríocht
699 * 533
Maitrís
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Cothromóid chomhuaineach
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Difreáil
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Comhtháthú
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Teorainneacha
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}