r=10*535134-2217*2489/sqrt{10*695135-(2489)^2-sqrt{10*607741-(2217)^2}} eching

$$r = \frac { 10 * 535134 - 2217 * 2489 } { \sqrt { 10 * 695135 - ( 2489 ) ^ { 2 } } - \sqrt { 10 * 607741 - ( 2217 ) ^ { 2 } } }$$

r uchun yechish

$$r = \frac{55591 {(\sqrt{756229} + \sqrt{1162321})}}{135364} \approx 799,887238416$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

5351340 hosil qilish uchun 10 va 535134 ni ko'paytirish.

$$r=\frac{5351340-2217\times 2489}{\sqrt{10\times 695135-2489^{2}}-\sqrt{10\times 607741-2217^{2}}}$$

5518113 hosil qilish uchun 2217 va 2489 ni ko'paytirish.

$$r=\frac{5351340-5518113}{\sqrt{10\times 695135-2489^{2}}-\sqrt{10\times 607741-2217^{2}}}$$

-166773 olish uchun 5351340 dan 5518113 ni ayirish.

$$r=\frac{-166773}{\sqrt{10\times 695135-2489^{2}}-\sqrt{10\times 607741-2217^{2}}}$$

6951350 hosil qilish uchun 10 va 695135 ni ko'paytirish.

$$r=\frac{-166773}{\sqrt{6951350-2489^{2}}-\sqrt{10\times 607741-2217^{2}}}$$

2 daraja ko‘rsatkichini 2489 ga hisoblang va 6195121 ni qiymatni oling.

$$r=\frac{-166773}{\sqrt{6951350-6195121}-\sqrt{10\times 607741-2217^{2}}}$$

756229 olish uchun 6951350 dan 6195121 ni ayirish.

$$r=\frac{-166773}{\sqrt{756229}-\sqrt{10\times 607741-2217^{2}}}$$

6077410 hosil qilish uchun 10 va 607741 ni ko'paytirish.

$$r=\frac{-166773}{\sqrt{756229}-\sqrt{6077410-2217^{2}}}$$

2 daraja ko‘rsatkichini 2217 ga hisoblang va 4915089 ni qiymatni oling.

$$r=\frac{-166773}{\sqrt{756229}-\sqrt{6077410-4915089}}$$

1162321 olish uchun 6077410 dan 4915089 ni ayirish.

$$r=\frac{-166773}{\sqrt{756229}-\sqrt{1162321}}$$

\frac{-166773}{\sqrt{756229}-\sqrt{1162321}} maxrajini \sqrt{756229}+\sqrt{1162321} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$r=\frac{-166773\left(\sqrt{756229}+\sqrt{1162321}\right)}{\left(\sqrt{756229}-\sqrt{1162321}\right)\left(\sqrt{756229}+\sqrt{1162321}\right)}$$

Hisoblang: \left(\sqrt{756229}-\sqrt{1162321}\right)\left(\sqrt{756229}+\sqrt{1162321}\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$r=\frac{-166773\left(\sqrt{756229}+\sqrt{1162321}\right)}{\left(\sqrt{756229}\right)^{2}-\left(\sqrt{1162321}\right)^{2}}$$

\sqrt{756229} kvadratini chiqarish. \sqrt{1162321} kvadratini chiqarish.

$$r=\frac{-166773\left(\sqrt{756229}+\sqrt{1162321}\right)}{756229-1162321}$$

-406092 olish uchun 756229 dan 1162321 ni ayirish.

$$r=\frac{-166773\left(\sqrt{756229}+\sqrt{1162321}\right)}{-406092}$$

\frac{55591}{135364}\left(\sqrt{756229}+\sqrt{1162321}\right) ni olish uchun -166773\left(\sqrt{756229}+\sqrt{1162321}\right) ni -406092 ga bo‘ling.

$$r=\frac{55591}{135364}\left(\sqrt{756229}+\sqrt{1162321}\right)$$

\frac{55591}{135364} ga \sqrt{756229}+\sqrt{1162321} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$r=\frac{55591}{135364}\sqrt{756229}+\frac{55591}{135364}\sqrt{1162321}$$

r'ni tayinlash

$$r≔\frac{55591\left(\sqrt{756229}+\sqrt{1162321}\right)}{135364}$$