x^2=9+(17-x2sqrt{x})*((7-x-2sqrt{x})-6*cos81^circ) eching

$$x ^ { 2 } = 9 + ( 17 - x 2 \sqrt { x } ) \times ( ( 7 - x - 2 \sqrt { x } ) - 6 \cdot \cos 81 ^ { \circ } )$$

x_2 uchun yechish

$$x_{2}=-\frac{-x^{2}-17x-34\sqrt{x}+112,04368456589644616}{\sqrt{x}\left(x+2\sqrt{x}-6,06139320975861448\right)}$$

$$x\neq -\frac{\sqrt{441337075609913405}}{125000000}+\frac{100767415121982681}{12500000000000000}\text{ and }x>0$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Evaluate trigonometric functions in the problem

$$x ^ {2} = 9 + {(17 - x 2 \sqrt{x})} \cdot {({(7 - x - 2 \sqrt{x})} - 6 \cdot 0,15643446504023092)}$$

0,93860679024138552 hosil qilish uchun 6 va 0,15643446504023092 ni ko'paytirish.

$$x^{2}=9+\left(17-x_{2}\sqrt{x}\right)\left(7-x-2\sqrt{x}-0,93860679024138552\right)$$

17-x_{2}\sqrt{x} ga 7-x-2\sqrt{x}-0,93860679024138552 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{2}=9+\left(17-x_{2}\sqrt{x}\right)\left(7-x-2\sqrt{x}\right)-0,93860679024138552\left(17-x_{2}\sqrt{x}\right)$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$9+\left(17-x_{2}\sqrt{x}\right)\left(7-x-2\sqrt{x}\right)-0,93860679024138552\left(17-x_{2}\sqrt{x}\right)=x^{2}$$

Ikkala tarafdan 9 ni ayirish.

$$\left(17-x_{2}\sqrt{x}\right)\left(7-x-2\sqrt{x}\right)-0,93860679024138552\left(17-x_{2}\sqrt{x}\right)=x^{2}-9$$

17-x_{2}\sqrt{x} ga 7-x-2\sqrt{x} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$119-17x-34\sqrt{x}-7x_{2}\sqrt{x}+xx_{2}\sqrt{x}+2x_{2}\left(\sqrt{x}\right)^{2}-0,93860679024138552\left(17-x_{2}\sqrt{x}\right)=x^{2}-9$$

2 daraja ko‘rsatkichini \sqrt{x} ga hisoblang va x ni qiymatni oling.

$$119-17x-34\sqrt{x}-7x_{2}\sqrt{x}+xx_{2}\sqrt{x}+2x_{2}x-0,93860679024138552\left(17-x_{2}\sqrt{x}\right)=x^{2}-9$$

-0,93860679024138552 ga 17-x_{2}\sqrt{x} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$119-17x-34\sqrt{x}-7x_{2}\sqrt{x}+xx_{2}\sqrt{x}+2x_{2}x-15,95631543410355384+0,93860679024138552x_{2}\sqrt{x}=x^{2}-9$$

103,04368456589644616 olish uchun 119 dan 15,95631543410355384 ni ayirish.

$$103,04368456589644616-17x-34\sqrt{x}-7x_{2}\sqrt{x}+xx_{2}\sqrt{x}+2x_{2}x+0,93860679024138552x_{2}\sqrt{x}=x^{2}-9$$

-6,06139320975861448x_{2}\sqrt{x} ni olish uchun -7x_{2}\sqrt{x} va 0,93860679024138552x_{2}\sqrt{x} ni birlashtirish.

$$103,04368456589644616-17x-34\sqrt{x}-6,06139320975861448x_{2}\sqrt{x}+xx_{2}\sqrt{x}+2x_{2}x=x^{2}-9$$

Ikkala tarafdan 103,04368456589644616 ni ayirish.

$$-17x-34\sqrt{x}-6,06139320975861448x_{2}\sqrt{x}+xx_{2}\sqrt{x}+2x_{2}x=x^{2}-9-103,04368456589644616$$

-112,04368456589644616 olish uchun -9 dan 103,04368456589644616 ni ayirish.

$$-17x-34\sqrt{x}-6,06139320975861448x_{2}\sqrt{x}+xx_{2}\sqrt{x}+2x_{2}x=x^{2}-112,04368456589644616$$

17x ni ikki tarafga qo’shing.

$$-34\sqrt{x}-6,06139320975861448x_{2}\sqrt{x}+xx_{2}\sqrt{x}+2x_{2}x=x^{2}-112,04368456589644616+17x$$

34\sqrt{x} ni ikki tarafga qo’shing.

$$-6,06139320975861448x_{2}\sqrt{x}+xx_{2}\sqrt{x}+2x_{2}x=x^{2}-112,04368456589644616+17x+34\sqrt{x}$$

x_{2}'ga ega bo'lgan barcha shartlarni birlashtirish.

$$\left(-6,06139320975861448\sqrt{x}+x\sqrt{x}+2x\right)x_{2}=x^{2}-112,04368456589644616+17x+34\sqrt{x}$$

Tenglama standart shaklda.

$$\left(\sqrt{x}x+2x-\frac{75767415121982681\sqrt{x}}{12500000000000000}\right)x_{2}=x^{2}+17x+34\sqrt{x}-112,04368456589644616$$

Ikki tarafini -6,06139320975861448\sqrt{x}+x\sqrt{x}+2x ga bo‘ling.

$$\frac{\left(\sqrt{x}x+2x-\frac{75767415121982681\sqrt{x}}{12500000000000000}\right)x_{2}}{\sqrt{x}x+2x-\frac{75767415121982681\sqrt{x}}{12500000000000000}}=\frac{x^{2}+17x+34\sqrt{x}-112,04368456589644616}{\sqrt{x}x+2x-\frac{75767415121982681\sqrt{x}}{12500000000000000}}$$

-6,06139320975861448\sqrt{x}+x\sqrt{x}+2x ga bo'lish -6,06139320975861448\sqrt{x}+x\sqrt{x}+2x ga ko'paytirishni bekor qiladi.

$$x_{2}=\frac{x^{2}+17x+34\sqrt{x}-112,04368456589644616}{\sqrt{x}x+2x-\frac{75767415121982681\sqrt{x}}{12500000000000000}}$$

x^{2}-112,04368456589644616+17x+34\sqrt{x} ni -6,06139320975861448\sqrt{x}+x\sqrt{x}+2x ga bo'lish.

$$x_{2}=\frac{x^{2}+17x+34\sqrt{x}-112,04368456589644616}{\sqrt{x}\left(x+2\sqrt{x}-6,06139320975861448\right)}$$