ແກ້ frac{7+3sqrt{5}}{3+sqrt{5}}-frac{7-3sqrt{5}}{3-sqrt{5}} | ແກ້ໄຂ frac{7+3sqrt{5}}{3+sqrt{5}}-frac{7-3sqrt{5}}{3-sqrt{5}}

ປະເມີນ

ຂັ້ນຕອນທາງອອກສັ້ນ

Quiz

Arithmetic

5 ບັນຫາທີ່ຄ້າຍຄືກັນກັບ:

ບັນຫາທີ່ຄ້າຍຄືກັນຈາກWeb Search

https://math.stackexchange.com/questions/2177155/the-expression-sqrt133-sqrt-frac233-sqrt13-3-sqrt-frac233

https://socratic.org/questions/57bd876a11ef6b7f9b3ba7f0

https://socratic.org/questions/how-do-you-order-the-following-from-least-to-greatest-sqrt-5-6-sqrt-19-7-sqrt-11

https://socratic.org/questions/how-do-you-evaluate-frac-a-sqrt-a-1-a-sqrt-a-frac-a-sqrt-a-1-a-sqrt-a

https://math.stackexchange.com/q/720867

https://math.stackexchange.com/questions/1929320/finding-the-two-planes-that-contain-a-given-line-and-form-the-same-angle-with-tw

ແບ່ງປັນ

ສໍາເນົາຄລິບ

\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}}

ໃຊ້ເຫດຜົນຕັດສິນຕົວຫານຂອງ \frac{7+3\sqrt{5}}{3+\sqrt{5}} ໂດຍການຫານຕົວເສດ ແລະ ຕົວຫານໂດຍ 3-\sqrt{5}.

\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}}

ພິຈາລະນາ \left(3+\sqrt{5}\right)\left(3-\sqrt{5}\right). ການຄູນສາມາດປ່ຽນເປັນຮາກອື່ນໂດຍໃຊ້ກົດ: \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}}

ຮາກທີ່ສອງຂອງຄ່າສະເລ່ຍ 3. ຮາກທີ່ສອງຂອງຄ່າສະເລ່ຍ \sqrt{5}.

\frac{\left(7+3\sqrt{5}\right)\left(3-\sqrt{5}\right)}{4}-\frac{7-3\sqrt{5}}{3-\sqrt{5}}

ລົບ 5 ອອກຈາກ 9 ເພື່ອໃຫ້ໄດ້ 4.

\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)}

ໃຊ້ເຫດຜົນຕັດສິນຕົວຫານຂອງ \frac{7-3\sqrt{5}}{3-\sqrt{5}} ໂດຍການຫານຕົວເສດ ແລະ ຕົວຫານໂດຍ 3+\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)}{3^{2}-\left(\sqrt{5}\right)^{2}}

ພິຈາລະນາ \left(3-\sqrt{5}\right)\left(3+\sqrt{5}\right). ການຄູນສາມາດປ່ຽນເປັນຮາກອື່ນໂດຍໃຊ້ກົດ: \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}

ຮາກທີ່ສອງຂອງຄ່າສະເລ່ຍ 3. ຮາກທີ່ສອງຂອງຄ່າສະເລ່ຍ \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}

ລົບ 5 ອອກຈາກ 9 ເພື່ອໃຫ້ໄດ້ 4.

\frac{\left(7+3\sqrt{5}\right)\left(3-\sqrt{5}\right)-\left(7-3\sqrt{5}\right)\left(3+\sqrt{5}\right)}{4}

ເນື່ອງຈາກ \frac{\left(7+3\sqrt{5}\right)\left(3-\sqrt{5}\right)}{4} ແລະ \frac{\left(7-3\sqrt{5}\right)\left(3+\sqrt{5}\right)}{4} ມີຕົວຫານດຽວກັນ, ໃຫ້ຫານພວກມັນໂດຍການຫານຈຳນວນທີ່ເປັນເສດໃນເລກເສດສ່ວນຂອງພວກມັນ.

\frac{21-7\sqrt{5}+9\sqrt{5}-15-21-7\sqrt{5}+9\sqrt{5}+15}{4}

ຄູນໃນເສດສ່ວນ \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}

ຄຳນວນໃນ 21-7\sqrt{5}+9\sqrt{5}-15-21-7\sqrt{5}+9\sqrt{5}+15.

\sqrt{5}

ຍົກເລີກ 4 ແລະ 4.