HB=1500/314*5*(5-sqrt{5^2-2295^2)} eching

$$H B = \frac { 1500 } { 314 \cdot 5 \cdot ( 5 - \sqrt { 5 ^ { 2 } - 2295 ^ { 2 } } ) }$$

B uchun yechish

$$B=\frac{10\left(1+2\sqrt{52670}i\right)}{11025639H}$$

$$H\neq 0$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

1570 hosil qilish uchun 5 va 314 ni ko'paytirish.

$$HB=\frac{1500}{1570\left(5-\sqrt{5^{2}-2295^{2}}\right)}$$

2 daraja ko‘rsatkichini 5 ga hisoblang va 25 ni qiymatni oling.

$$HB=\frac{1500}{1570\left(5-\sqrt{25-2295^{2}}\right)}$$

2 daraja ko‘rsatkichini 2295 ga hisoblang va 5267025 ni qiymatni oling.

$$HB=\frac{1500}{1570\left(5-\sqrt{25-5267025}\right)}$$

-5267000 olish uchun 25 dan 5267025 ni ayirish.

$$HB=\frac{1500}{1570\left(5-\sqrt{-5267000}\right)}$$

Faktor: -5267000=\left(10i\right)^{2}\times 52670. \sqrt{\left(10i\right)^{2}\times 52670} koʻpaytmasining kvadrat ildizini \sqrt{\left(10i\right)^{2}}\sqrt{52670} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. \left(10i\right)^{2} ning kvadrat ildizini chiqarish.

$$HB=\frac{1500}{1570\left(5-10i\sqrt{52670}\right)}$$

1570 ga 5-10i\sqrt{52670} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$HB=\frac{1500}{7850-15700i\sqrt{52670}}$$

\frac{1500}{7850-15700i\sqrt{52670}} maxrajini 7850+15700i\sqrt{52670} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$HB=\frac{1500\left(7850+15700i\sqrt{52670}\right)}{\left(7850-15700i\sqrt{52670}\right)\left(7850+15700i\sqrt{52670}\right)}$$

Hisoblang: \left(7850-15700i\sqrt{52670}\right)\left(7850+15700i\sqrt{52670}\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$HB=\frac{1500\left(7850+15700i\sqrt{52670}\right)}{7850^{2}-\left(-15700i\sqrt{52670}\right)^{2}}$$

2 daraja ko‘rsatkichini 7850 ga hisoblang va 61622500 ni qiymatni oling.

$$HB=\frac{1500\left(7850+15700i\sqrt{52670}\right)}{61622500-\left(-15700i\sqrt{52670}\right)^{2}}$$

\left(-15700i\sqrt{52670}\right)^{2} ni kengaytirish.

$$HB=\frac{1500\left(7850+15700i\sqrt{52670}\right)}{61622500-\left(-15700i\right)^{2}\left(\sqrt{52670}\right)^{2}}$$

2 daraja ko‘rsatkichini -15700i ga hisoblang va -246490000 ni qiymatni oling.

$$HB=\frac{1500\left(7850+15700i\sqrt{52670}\right)}{61622500-\left(-246490000\left(\sqrt{52670}\right)^{2}\right)}$$

\sqrt{52670} kvadrati – 52670.

$$HB=\frac{1500\left(7850+15700i\sqrt{52670}\right)}{61622500-\left(-246490000\times 52670\right)}$$

-12982628300000 hosil qilish uchun -246490000 va 52670 ni ko'paytirish.

$$HB=\frac{1500\left(7850+15700i\sqrt{52670}\right)}{61622500-\left(-12982628300000\right)}$$

12982628300000 hosil qilish uchun -1 va -12982628300000 ni ko'paytirish.

$$HB=\frac{1500\left(7850+15700i\sqrt{52670}\right)}{61622500+12982628300000}$$

12982689922500 olish uchun 61622500 va 12982628300000'ni qo'shing.

$$HB=\frac{1500\left(7850+15700i\sqrt{52670}\right)}{12982689922500}$$

\frac{1}{8655126615}\left(7850+15700i\sqrt{52670}\right) ni olish uchun 1500\left(7850+15700i\sqrt{52670}\right) ni 12982689922500 ga bo‘ling.

$$HB=\frac{1}{8655126615}\left(7850+15700i\sqrt{52670}\right)$$

\frac{1}{8655126615} ga 7850+15700i\sqrt{52670} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$HB=\frac{10}{11025639}+\frac{20}{11025639}i\sqrt{52670}$$

Shartlarni qayta saralash.

$$BH=\frac{10}{11025639}+\frac{20}{11025639}\sqrt{52670}i$$

Tenglama standart shaklda.

$$HB=\frac{10+20\sqrt{52670}i}{11025639}$$

Ikki tarafini H ga bo‘ling.

$$\frac{HB}{H}=\frac{10+20\sqrt{52670}i}{11025639H}$$

H ga bo'lish H ga ko'paytirishni bekor qiladi.

$$B=\frac{10+20\sqrt{52670}i}{11025639H}$$

\frac{10+20i\sqrt{52670}}{11025639} ni H ga bo'lish.

$$B=\frac{10\left(1+2\sqrt{52670}i\right)}{11025639H}$$

H uchun yechish

$$H=\frac{10\left(1+2\sqrt{52670}i\right)}{11025639B}$$

$$B\neq 0$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

1570 hosil qilish uchun 5 va 314 ni ko'paytirish.

$$HB=\frac{1500}{1570\left(5-\sqrt{5^{2}-2295^{2}}\right)}$$

2 daraja ko‘rsatkichini 5 ga hisoblang va 25 ni qiymatni oling.

$$HB=\frac{1500}{1570\left(5-\sqrt{25-2295^{2}}\right)}$$

2 daraja ko‘rsatkichini 2295 ga hisoblang va 5267025 ni qiymatni oling.

$$HB=\frac{1500}{1570\left(5-\sqrt{25-5267025}\right)}$$

-5267000 olish uchun 25 dan 5267025 ni ayirish.

$$HB=\frac{1500}{1570\left(5-\sqrt{-5267000}\right)}$$

Faktor: -5267000=\left(10i\right)^{2}\times 52670. \sqrt{\left(10i\right)^{2}\times 52670} koʻpaytmasining kvadrat ildizini \sqrt{\left(10i\right)^{2}}\sqrt{52670} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. \left(10i\right)^{2} ning kvadrat ildizini chiqarish.

$$HB=\frac{1500}{1570\left(5-10i\sqrt{52670}\right)}$$

1570 ga 5-10i\sqrt{52670} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$HB=\frac{1500}{7850-15700i\sqrt{52670}}$$

\frac{1500}{7850-15700i\sqrt{52670}} maxrajini 7850+15700i\sqrt{52670} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$HB=\frac{1500\left(7850+15700i\sqrt{52670}\right)}{\left(7850-15700i\sqrt{52670}\right)\left(7850+15700i\sqrt{52670}\right)}$$

Hisoblang: \left(7850-15700i\sqrt{52670}\right)\left(7850+15700i\sqrt{52670}\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$HB=\frac{1500\left(7850+15700i\sqrt{52670}\right)}{7850^{2}-\left(-15700i\sqrt{52670}\right)^{2}}$$

2 daraja ko‘rsatkichini 7850 ga hisoblang va 61622500 ni qiymatni oling.

$$HB=\frac{1500\left(7850+15700i\sqrt{52670}\right)}{61622500-\left(-15700i\sqrt{52670}\right)^{2}}$$

\left(-15700i\sqrt{52670}\right)^{2} ni kengaytirish.

$$HB=\frac{1500\left(7850+15700i\sqrt{52670}\right)}{61622500-\left(-15700i\right)^{2}\left(\sqrt{52670}\right)^{2}}$$

2 daraja ko‘rsatkichini -15700i ga hisoblang va -246490000 ni qiymatni oling.

$$HB=\frac{1500\left(7850+15700i\sqrt{52670}\right)}{61622500-\left(-246490000\left(\sqrt{52670}\right)^{2}\right)}$$

\sqrt{52670} kvadrati – 52670.

$$HB=\frac{1500\left(7850+15700i\sqrt{52670}\right)}{61622500-\left(-246490000\times 52670\right)}$$

-12982628300000 hosil qilish uchun -246490000 va 52670 ni ko'paytirish.

$$HB=\frac{1500\left(7850+15700i\sqrt{52670}\right)}{61622500-\left(-12982628300000\right)}$$

12982628300000 hosil qilish uchun -1 va -12982628300000 ni ko'paytirish.

$$HB=\frac{1500\left(7850+15700i\sqrt{52670}\right)}{61622500+12982628300000}$$

12982689922500 olish uchun 61622500 va 12982628300000'ni qo'shing.

$$HB=\frac{1500\left(7850+15700i\sqrt{52670}\right)}{12982689922500}$$

\frac{1}{8655126615}\left(7850+15700i\sqrt{52670}\right) ni olish uchun 1500\left(7850+15700i\sqrt{52670}\right) ni 12982689922500 ga bo‘ling.

$$HB=\frac{1}{8655126615}\left(7850+15700i\sqrt{52670}\right)$$

\frac{1}{8655126615} ga 7850+15700i\sqrt{52670} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$HB=\frac{10}{11025639}+\frac{20}{11025639}i\sqrt{52670}$$

Shartlarni qayta saralash.

$$BH=\frac{10}{11025639}+\frac{20}{11025639}\sqrt{52670}i$$

Tenglama standart shaklda.

$$BH=\frac{10+20\sqrt{52670}i}{11025639}$$

Ikki tarafini B ga bo‘ling.

$$\frac{BH}{B}=\frac{10+20\sqrt{52670}i}{11025639B}$$

B ga bo'lish B ga ko'paytirishni bekor qiladi.

$$H=\frac{10+20\sqrt{52670}i}{11025639B}$$

\frac{10+20i\sqrt{52670}}{11025639} ni B ga bo'lish.

$$H=\frac{10\left(1+2\sqrt{52670}i\right)}{11025639B}$$