quadtext{36If}frac{sqrt{7}-2}{sqrt{7}+2}=asqrt{7}+b eching

$$\quad \text { 36 If } \frac { \sqrt { 7 } - 2 } { \sqrt { 7 } + 2 } = a \sqrt { 7 } + b$$

I uchun yechish (complex solution)

$$\left\{\begin{matrix}I=\frac{4\sqrt{7}b+11\sqrt{7}a+11b+28a}{108f}\text{, }&f\neq 0\\I\in \mathrm{C}\text{, }&a=-\frac{\sqrt{7}b}{7}\text{ and }f=0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

\frac{\sqrt{7}-2}{\sqrt{7}+2} maxrajini \sqrt{7}-2 orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$36If\times \frac{\left(\sqrt{7}-2\right)\left(\sqrt{7}-2\right)}{\left(\sqrt{7}+2\right)\left(\sqrt{7}-2\right)}=a\sqrt{7}+b$$

Hisoblang: \left(\sqrt{7}+2\right)\left(\sqrt{7}-2\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$36If\times \frac{\left(\sqrt{7}-2\right)\left(\sqrt{7}-2\right)}{\left(\sqrt{7}\right)^{2}-2^{2}}=a\sqrt{7}+b$$

\sqrt{7} kvadratini chiqarish. 2 kvadratini chiqarish.

$$36If\times \frac{\left(\sqrt{7}-2\right)\left(\sqrt{7}-2\right)}{7-4}=a\sqrt{7}+b$$

3 olish uchun 7 dan 4 ni ayirish.

$$36If\times \frac{\left(\sqrt{7}-2\right)\left(\sqrt{7}-2\right)}{3}=a\sqrt{7}+b$$

\left(\sqrt{7}-2\right)^{2} hosil qilish uchun \sqrt{7}-2 va \sqrt{7}-2 ni ko'paytirish.

$$36If\times \frac{\left(\sqrt{7}-2\right)^{2}}{3}=a\sqrt{7}+b$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(\sqrt{7}-2\right)^{2} kengaytirilishi uchun ishlating.

$$36If\times \frac{\left(\sqrt{7}\right)^{2}-4\sqrt{7}+4}{3}=a\sqrt{7}+b$$

\sqrt{7} kvadrati – 7.

$$36If\times \frac{7-4\sqrt{7}+4}{3}=a\sqrt{7}+b$$

11 olish uchun 7 va 4'ni qo'shing.

$$36If\times \frac{11-4\sqrt{7}}{3}=a\sqrt{7}+b$$

36 va 3 ichida eng katta umumiy 3 faktorini bekor qiling.

$$12\left(11-4\sqrt{7}\right)If=a\sqrt{7}+b$$

12 ga 11-4\sqrt{7} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(132-48\sqrt{7}\right)If=a\sqrt{7}+b$$

132-48\sqrt{7} ga I ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(132I-48\sqrt{7}I\right)f=a\sqrt{7}+b$$

132I-48\sqrt{7}I ga f ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$132If-48\sqrt{7}If=a\sqrt{7}+b$$

I'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(132f-48\sqrt{7}f\right)I=a\sqrt{7}+b$$

Tenglama standart shaklda.

$$\left(-48\sqrt{7}f+132f\right)I=\sqrt{7}a+b$$

Ikki tarafini 132f-48\sqrt{7}f ga bo‘ling.

$$\frac{\left(-48\sqrt{7}f+132f\right)I}{-48\sqrt{7}f+132f}=\frac{\sqrt{7}a+b}{-48\sqrt{7}f+132f}$$

132f-48\sqrt{7}f ga bo'lish 132f-48\sqrt{7}f ga ko'paytirishni bekor qiladi.

$$I=\frac{\sqrt{7}a+b}{-48\sqrt{7}f+132f}$$

a\sqrt{7}+b ni 132f-48\sqrt{7}f ga bo'lish.

$$I=\frac{\left(4\sqrt{7}+11\right)\left(\sqrt{7}a+b\right)}{108f}$$

I uchun yechish

$$\left\{\begin{matrix}I=\frac{4\sqrt{7}b+11\sqrt{7}a+11b+28a}{108f}\text{, }&f\neq 0\\I\in \mathrm{R}\text{, }&a=-\frac{\sqrt{7}b}{7}\text{ and }f=0\end{matrix}\right,$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

\frac{\sqrt{7}-2}{\sqrt{7}+2} maxrajini \sqrt{7}-2 orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$36If\times \frac{\left(\sqrt{7}-2\right)\left(\sqrt{7}-2\right)}{\left(\sqrt{7}+2\right)\left(\sqrt{7}-2\right)}=a\sqrt{7}+b$$

Hisoblang: \left(\sqrt{7}+2\right)\left(\sqrt{7}-2\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$36If\times \frac{\left(\sqrt{7}-2\right)\left(\sqrt{7}-2\right)}{\left(\sqrt{7}\right)^{2}-2^{2}}=a\sqrt{7}+b$$

\sqrt{7} kvadratini chiqarish. 2 kvadratini chiqarish.

$$36If\times \frac{\left(\sqrt{7}-2\right)\left(\sqrt{7}-2\right)}{7-4}=a\sqrt{7}+b$$

3 olish uchun 7 dan 4 ni ayirish.

$$36If\times \frac{\left(\sqrt{7}-2\right)\left(\sqrt{7}-2\right)}{3}=a\sqrt{7}+b$$

\left(\sqrt{7}-2\right)^{2} hosil qilish uchun \sqrt{7}-2 va \sqrt{7}-2 ni ko'paytirish.

$$36If\times \frac{\left(\sqrt{7}-2\right)^{2}}{3}=a\sqrt{7}+b$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(\sqrt{7}-2\right)^{2} kengaytirilishi uchun ishlating.

$$36If\times \frac{\left(\sqrt{7}\right)^{2}-4\sqrt{7}+4}{3}=a\sqrt{7}+b$$

\sqrt{7} kvadrati – 7.

$$36If\times \frac{7-4\sqrt{7}+4}{3}=a\sqrt{7}+b$$

11 olish uchun 7 va 4'ni qo'shing.

$$36If\times \frac{11-4\sqrt{7}}{3}=a\sqrt{7}+b$$

36 va 3 ichida eng katta umumiy 3 faktorini bekor qiling.

$$12\left(11-4\sqrt{7}\right)If=a\sqrt{7}+b$$

12 ga 11-4\sqrt{7} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(132-48\sqrt{7}\right)If=a\sqrt{7}+b$$

132-48\sqrt{7} ga I ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(132I-48\sqrt{7}I\right)f=a\sqrt{7}+b$$

132I-48\sqrt{7}I ga f ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$132If-48\sqrt{7}If=a\sqrt{7}+b$$

I'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(132f-48\sqrt{7}f\right)I=a\sqrt{7}+b$$

Tenglama standart shaklda.

$$\left(-48\sqrt{7}f+132f\right)I=\sqrt{7}a+b$$

Ikki tarafini 132f-48\sqrt{7}f ga bo‘ling.

$$\frac{\left(-48\sqrt{7}f+132f\right)I}{-48\sqrt{7}f+132f}=\frac{\sqrt{7}a+b}{-48\sqrt{7}f+132f}$$

132f-48\sqrt{7}f ga bo'lish 132f-48\sqrt{7}f ga ko'paytirishni bekor qiladi.

$$I=\frac{\sqrt{7}a+b}{-48\sqrt{7}f+132f}$$

a\sqrt{7}+b ni 132f-48\sqrt{7}f ga bo'lish.

$$I=\frac{\left(4\sqrt{7}+11\right)\left(\sqrt{7}a+b\right)}{108f}$$

a uchun yechish

$$a=-\frac{\sqrt{7}\left(48\sqrt{7}If-132If+b\right)}{7}$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

\frac{\sqrt{7}-2}{\sqrt{7}+2} maxrajini \sqrt{7}-2 orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$36If\times \frac{\left(\sqrt{7}-2\right)\left(\sqrt{7}-2\right)}{\left(\sqrt{7}+2\right)\left(\sqrt{7}-2\right)}=a\sqrt{7}+b$$

Hisoblang: \left(\sqrt{7}+2\right)\left(\sqrt{7}-2\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$36If\times \frac{\left(\sqrt{7}-2\right)\left(\sqrt{7}-2\right)}{\left(\sqrt{7}\right)^{2}-2^{2}}=a\sqrt{7}+b$$

\sqrt{7} kvadratini chiqarish. 2 kvadratini chiqarish.

$$36If\times \frac{\left(\sqrt{7}-2\right)\left(\sqrt{7}-2\right)}{7-4}=a\sqrt{7}+b$$

3 olish uchun 7 dan 4 ni ayirish.

$$36If\times \frac{\left(\sqrt{7}-2\right)\left(\sqrt{7}-2\right)}{3}=a\sqrt{7}+b$$

\left(\sqrt{7}-2\right)^{2} hosil qilish uchun \sqrt{7}-2 va \sqrt{7}-2 ni ko'paytirish.

$$36If\times \frac{\left(\sqrt{7}-2\right)^{2}}{3}=a\sqrt{7}+b$$

\left(a-b\right)^{2}=a^{2}-2ab+b^{2} binom teoremasini \left(\sqrt{7}-2\right)^{2} kengaytirilishi uchun ishlating.

$$36If\times \frac{\left(\sqrt{7}\right)^{2}-4\sqrt{7}+4}{3}=a\sqrt{7}+b$$

\sqrt{7} kvadrati – 7.

$$36If\times \frac{7-4\sqrt{7}+4}{3}=a\sqrt{7}+b$$

11 olish uchun 7 va 4'ni qo'shing.

$$36If\times \frac{11-4\sqrt{7}}{3}=a\sqrt{7}+b$$

36 va 3 ichida eng katta umumiy 3 faktorini bekor qiling.

$$12\left(11-4\sqrt{7}\right)If=a\sqrt{7}+b$$

12 ga 11-4\sqrt{7} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(132-48\sqrt{7}\right)If=a\sqrt{7}+b$$

132-48\sqrt{7} ga I ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\left(132I-48\sqrt{7}I\right)f=a\sqrt{7}+b$$

132I-48\sqrt{7}I ga f ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$132If-48\sqrt{7}If=a\sqrt{7}+b$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$a\sqrt{7}+b=132If-48\sqrt{7}If$$

Ikkala tarafdan b ni ayirish.

$$a\sqrt{7}=132If-48\sqrt{7}If-b$$

Tenglama standart shaklda.

$$\sqrt{7}a=-48\sqrt{7}If+132If-b$$

Ikki tarafini \sqrt{7} ga bo‘ling.

$$\frac{\sqrt{7}a}{\sqrt{7}}=\frac{-48\sqrt{7}If+132If-b}{\sqrt{7}}$$

\sqrt{7} ga bo'lish \sqrt{7} ga ko'paytirishni bekor qiladi.

$$a=\frac{-48\sqrt{7}If+132If-b}{\sqrt{7}}$$

-b+132fI-48\sqrt{7}fI ni \sqrt{7} ga bo'lish.

$$a=\frac{\sqrt{7}\left(-48\sqrt{7}If+132If-b\right)}{7}$$