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\frac{\left(4+\sqrt{5}\right)\left(4+\sqrt{5}\right)}{\left(4-\sqrt{5}\right)\left(4+\sqrt{5}\right)}+\frac{4-\sqrt{5}}{4+\sqrt{5}}
\frac{4+\sqrt{5}}{4-\sqrt{5}} maxrajini 4+\sqrt{5} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.
\frac{\left(4+\sqrt{5}\right)\left(4+\sqrt{5}\right)}{4^{2}-\left(\sqrt{5}\right)^{2}}+\frac{4-\sqrt{5}}{4+\sqrt{5}}
Hisoblang: \left(4-\sqrt{5}\right)\left(4+\sqrt{5}\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
\frac{\left(4+\sqrt{5}\right)\left(4+\sqrt{5}\right)}{16-5}+\frac{4-\sqrt{5}}{4+\sqrt{5}}
4 kvadratini chiqarish. \sqrt{5} kvadratini chiqarish.
\frac{\left(4+\sqrt{5}\right)\left(4+\sqrt{5}\right)}{11}+\frac{4-\sqrt{5}}{4+\sqrt{5}}
11 olish uchun 16 dan 5 ni ayirish.
\frac{\left(4+\sqrt{5}\right)^{2}}{11}+\frac{4-\sqrt{5}}{4+\sqrt{5}}
\left(4+\sqrt{5}\right)^{2} hosil qilish uchun 4+\sqrt{5} va 4+\sqrt{5} ni ko'paytirish.
\frac{16+8\sqrt{5}+\left(\sqrt{5}\right)^{2}}{11}+\frac{4-\sqrt{5}}{4+\sqrt{5}}
\left(a+b\right)^{2}=a^{2}+2ab+b^{2} binom teoremasini \left(4+\sqrt{5}\right)^{2} kengaytirilishi uchun ishlating.
\frac{16+8\sqrt{5}+5}{11}+\frac{4-\sqrt{5}}{4+\sqrt{5}}
\sqrt{5} kvadrati – 5.
\frac{21+8\sqrt{5}}{11}+\frac{4-\sqrt{5}}{4+\sqrt{5}}
21 olish uchun 16 va 5'ni qo'shing.
\frac{21+8\sqrt{5}}{11}+\frac{\left(4-\sqrt{5}\right)\left(4-\sqrt{5}\right)}{\left(4+\sqrt{5}\right)\left(4-\sqrt{5}\right)}
\frac{4-\sqrt{5}}{4+\sqrt{5}} maxrajini 4-\sqrt{5} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.
\frac{21+8\sqrt{5}}{11}+\frac{\left(4-\sqrt{5}\right)\left(4-\sqrt{5}\right)}{4^{2}-\left(\sqrt{5}\right)^{2}}
Hisoblang: \left(4+\sqrt{5}\right)\left(4-\sqrt{5}\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
\frac{21+8\sqrt{5}}{11}+\frac{\left(4-\sqrt{5}\right)\left(4-\sqrt{5}\right)}{16-5}
4 kvadratini chiqarish. \sqrt{5} kvadratini chiqarish.
\frac{21+8\sqrt{5}}{11}+\frac{\left(4-\sqrt{5}\right)\left(4-\sqrt{5}\right)}{11}
11 olish uchun 16 dan 5 ni ayirish.
\frac{21+8\sqrt{5}}{11}+\frac{\left(4-\sqrt{5}\right)^{2}}{11}
\left(4-\sqrt{5}\right)^{2} hosil qilish uchun 4-\sqrt{5} va 4-\sqrt{5} ni ko'paytirish.
\frac{21+8\sqrt{5}}{11}+\frac{16-8\sqrt{5}+\left(\sqrt{5}\right)^{2}}{11}
\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(4-\sqrt{5}\right)^{2} kengaytirilishi uchun ishlating.
\frac{21+8\sqrt{5}}{11}+\frac{16-8\sqrt{5}+5}{11}
\sqrt{5} kvadrati – 5.
\frac{21+8\sqrt{5}}{11}+\frac{21-8\sqrt{5}}{11}
21 olish uchun 16 va 5'ni qo'shing.
\frac{21+8\sqrt{5}+21-8\sqrt{5}}{11}
\frac{21+8\sqrt{5}}{11} va \frac{21-8\sqrt{5}}{11} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.
\frac{42}{11}
21+8\sqrt{5}+21-8\sqrt{5} hisob-kitobini qiling.