Selesaikan frac{886731088897-627013566048sqrt{2}}{886731088897+627013566048sqrt{2}}

$$\frac{ 886731088897-627013566048 \sqrt{ 2 } }{ 886731088897+627013566048 \sqrt{ 2 } }$$

Nilaikan

$$1572584048032918633353217-1111984844349868137938112\sqrt{2}\approx -268435456$$

Langkah Penyelesaian

Nisbahkan penyebut \frac{886731088897-627013566048\sqrt{2}}{886731088897+627013566048\sqrt{2}} dengan mendarabkan pembilang dan penyebut dengan 886731088897-627013566048\sqrt{2}.

$$\frac{\left(886731088897-627013566048\sqrt{2}\right)\left(886731088897-627013566048\sqrt{2}\right)}{\left(886731088897+627013566048\sqrt{2}\right)\left(886731088897-627013566048\sqrt{2}\right)}$$

Pertimbangkan \left(886731088897+627013566048\sqrt{2}\right)\left(886731088897-627013566048\sqrt{2}\right). Pendaraban boleh diubah menjadi perbezaan kuasa dua dengan menggunakan peraturan: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\left(886731088897-627013566048\sqrt{2}\right)\left(886731088897-627013566048\sqrt{2}\right)}{886731088897^{2}-\left(627013566048\sqrt{2}\right)^{2}}$$

Darabkan 886731088897-627013566048\sqrt{2} dan 886731088897-627013566048\sqrt{2} untuk mendapatkan \left(886731088897-627013566048\sqrt{2}\right)^{2}.

$$\frac{\left(886731088897-627013566048\sqrt{2}\right)^{2}}{886731088897^{2}-\left(627013566048\sqrt{2}\right)^{2}}$$

Gunakan teorem binomial \left(a-b\right)^{2}=a^{2}-2ab+b^{2} untuk mengembangkan \left(886731088897-627013566048\sqrt{2}\right)^{2}.

$$\frac{786292024016459316676609-1111984844349868137938112\sqrt{2}+393146012008229658338304\left(\sqrt{2}\right)^{2}}{886731088897^{2}-\left(627013566048\sqrt{2}\right)^{2}}$$

Punca kuasa untuk \sqrt{2} ialah 2.

$$\frac{786292024016459316676609-1111984844349868137938112\sqrt{2}+393146012008229658338304\times 2}{886731088897^{2}-\left(627013566048\sqrt{2}\right)^{2}}$$

Darabkan 393146012008229658338304 dan 2 untuk mendapatkan 786292024016459316676608.

$$\frac{786292024016459316676609-1111984844349868137938112\sqrt{2}+786292024016459316676608}{886731088897^{2}-\left(627013566048\sqrt{2}\right)^{2}}$$

Tambahkan 786292024016459316676609 dan 786292024016459316676608 untuk dapatkan 1572584048032918633353217.

$$\frac{1572584048032918633353217-1111984844349868137938112\sqrt{2}}{886731088897^{2}-\left(627013566048\sqrt{2}\right)^{2}}$$

Kira 886731088897 dikuasakan 2 dan dapatkan 786292024016459316676609.

$$\frac{1572584048032918633353217-1111984844349868137938112\sqrt{2}}{786292024016459316676609-\left(627013566048\sqrt{2}\right)^{2}}$$

Kembangkan \left(627013566048\sqrt{2}\right)^{2}.

$$\frac{1572584048032918633353217-1111984844349868137938112\sqrt{2}}{786292024016459316676609-627013566048^{2}\left(\sqrt{2}\right)^{2}}$$

Kira 627013566048 dikuasakan 2 dan dapatkan 393146012008229658338304.

$$\frac{1572584048032918633353217-1111984844349868137938112\sqrt{2}}{786292024016459316676609-393146012008229658338304\left(\sqrt{2}\right)^{2}}$$

Punca kuasa untuk \sqrt{2} ialah 2.

$$\frac{1572584048032918633353217-1111984844349868137938112\sqrt{2}}{786292024016459316676609-393146012008229658338304\times 2}$$

Darabkan 393146012008229658338304 dan 2 untuk mendapatkan 786292024016459316676608.

$$\frac{1572584048032918633353217-1111984844349868137938112\sqrt{2}}{786292024016459316676609-786292024016459316676608}$$

Tolak 786292024016459316676608 daripada 786292024016459316676609 untuk mendapatkan 1.

$$\frac{1572584048032918633353217-1111984844349868137938112\sqrt{2}}{1}$$

Apa-apa sahaja yang dibahagikan dengan satu menjadi nombor tersebut.

$$1572584048032918633353217-1111984844349868137938112\sqrt{2}$$