Whakaoti i te 46/60=x^2+11547^2-2x11547cos(36)

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

Whakaoti mō x_11547

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

Ngā Upane mō te Whakaoti Whārite Rārangi

Evaluate trigonometric functions in the problem

$$\frac{46}{60} = {(x)} ^ {2} + {(11547)} ^ {2} - 2 x 11547 \cdot 0.8090169943749475$$

Whakahekea te hautanga \frac{46}{60} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{23}{30}=x^{2}+11547^{2}-2x_{11547}\times 0.8090169943749475$$

Tātaihia te 11547 mā te pū o 2, kia riro ko 133333209.

$$\frac{23}{30}=x^{2}[phone]x_{11547}\times 0.8090169943749475$$

Whakareatia te 2 ki te 0.8090169943749475, ka 1.618033988749895.

$$\frac{23}{30}=x^{2}[phone]-1.618033988749895x_{11547}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$x^{2}[phone]-1.618033988749895x_{11547}=\frac{23}{30}$$

Tangohia te x^{2} mai i ngā taha e rua.

$$133333209-1.618033988749895x_{11547}=\frac{23}{30}-x^{2}$$

Tangohia te 133333209 mai i ngā taha e rua.

$$-1.618033988749895x_{11547}=\frac{23}{30}-x^{2}-133333209$$

Tangohia te 133333209 i te \frac{23}{30}, ka -\frac{3999996247}{30}.

$$-1.618033988749895x_{11547}=-\frac{3999996247}{30}-x^{2}$$

He hanga arowhānui tō te whārite.

$$-1.618033988749895x_{11547}=-x^{2}-\frac{3999996247}{30}$$

Whakawehea ngā taha e rua o te whārite ki te -1.618033988749895, he ōrite ki te whakarea i ngā taha e rua ki te tau huripoki o te hautanga.

$$\frac{-1.618033988749895x_{11547}}{-1.618033988749895}=\frac{-x^{2}-\frac{3999996247}{30}}{-1.618033988749895}$$

Mā te whakawehe ki te -1.618033988749895 ka wetekia te whakareanga ki te -1.618033988749895.

$$x_{11547}=\frac{-x^{2}-\frac{3999996247}{30}}{-1.618033988749895}$$

Whakawehe -\frac{3999996247}{30}-x^{2} ki te -1.618033988749895 mā te whakarea -\frac{3999996247}{30}-x^{2} ki te tau huripoki o -1.618033988749895.

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

Whakaoti mō x

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

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