46/60=x^2+11547^2-2x11547cos(36) eching

$$\frac{ 46 }{ 60 } = { x }^{ 2 } + { 11547 }^{ 2 } -2x11547 \cos ( 36 )$$

x_11547 uchun yechish

$$x_{11547}=\frac{200000000000000x^{2}}{323606797749979}+\frac{79999924940000000000000}{970820393249937}$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Evaluate trigonometric functions in the problem

$$\frac{46}{60} = {(x)} ^ {2} + {(11547)} ^ {2} - 2 x 11547 \cdot 0,8090169943749475$$

\frac{46}{60} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{23}{30}=x^{2}+11547^{2}-2x_{11547}\times 0,8090169943749475$$

2 daraja ko‘rsatkichini 11547 ga hisoblang va 133333209 ni qiymatni oling.

$$\frac{23}{30}=x^{2}[phone]x_{11547}\times 0,8090169943749475$$

1,618033988749895 hosil qilish uchun 2 va 0,8090169943749475 ni ko'paytirish.

$$\frac{23}{30}=x^{2}[phone]-1,618033988749895x_{11547}$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$x^{2}[phone]-1,618033988749895x_{11547}=\frac{23}{30}$$

Ikkala tarafdan x^{2} ni ayirish.

$$133333209-1,618033988749895x_{11547}=\frac{23}{30}-x^{2}$$

Ikkala tarafdan 133333209 ni ayirish.

$$-1,618033988749895x_{11547}=\frac{23}{30}-x^{2}-133333209$$

-\frac{3999996247}{30} olish uchun \frac{23}{30} dan 133333209 ni ayirish.

$$-1,618033988749895x_{11547}=-\frac{3999996247}{30}-x^{2}$$

Tenglama standart shaklda.

$$-1,618033988749895x_{11547}=-x^{2}-\frac{3999996247}{30}$$

Tenglamaning ikki tarafini -1,618033988749895 ga bo'lish, bu kasrni qaytarish orqali ikkala tarafga ko'paytirish bilan aynidir.

$$\frac{-1,618033988749895x_{11547}}{-1,618033988749895}=\frac{-x^{2}-\frac{3999996247}{30}}{-1,618033988749895}$$

-1,618033988749895 ga bo'lish -1,618033988749895 ga ko'paytirishni bekor qiladi.

$$x_{11547}=\frac{-x^{2}-\frac{3999996247}{30}}{-1,618033988749895}$$

-\frac{3999996247}{30}-x^{2} ni -1,618033988749895 ga bo'lish -\frac{3999996247}{30}-x^{2} ga k'paytirish -1,618033988749895 ga qaytarish.

$$x_{11547}=\frac{200000000000000x^{2}}{323606797749979}+\frac{79999924940000000000000}{970820393249937}$$

x uchun yechish

$$x=\frac{\sqrt{5824922359499622x_{11547}-479999549640000000000000}}{60000000}$$

$$x=-\frac{\sqrt{5824922359499622x_{11547}-479999549640000000000000}}{60000000}\text{, }x_{11547}\geq \frac{79999924940000000000000}{970820393249937}$$