Datrys (12/y)^2+5y^2=16

$$( \frac { 12 } { y } ) ^ { 2 } + 5 y ^ { 2 } = 16$$

Datrys ar gyfer y

$$y=\frac{2\sqrt{3}\times 5^{\frac{3}{4}}e^{-\frac{\arctan(\frac{\sqrt{41}}{2})i}{2}}}{5}\approx 1.866355157-1.372327065i$$

$$y=\frac{2\sqrt{3}\times 5^{\frac{3}{4}}e^{\frac{-\arctan(\frac{\sqrt{41}}{2})i+2\pi i}{2}}}{5}\approx -1.866355157+1.372327065i$$

$$y=\frac{2\sqrt{3}\times 5^{\frac{3}{4}}e^{\frac{\arctan(\frac{\sqrt{41}}{2})i}{2}}}{5}\approx 1.866355157+1.372327065i$$

$$y=\frac{2\sqrt{3}\times 5^{\frac{3}{4}}e^{\frac{\arctan(\frac{\sqrt{41}}{2})i+2\pi i}{2}}}{5}\approx -1.866355157-1.372327065i$$

Camau gan Ddefnyddio’r Fformiwla Cwadratig

I godi \frac{12}{y} i bŵer, codwch y rhifiadur a'r enwadur i bŵer ac yna rhannwch nhw.

$$\frac{12^{2}}{y^{2}}+5y^{2}=16$$

I ychwanegu neu dynnu mynegiannau, rhaid i chi eu ehangu i wneud eu enwaduron yr un fath. Lluoswch 5y^{2} â \frac{y^{2}}{y^{2}}.

$$\frac{12^{2}}{y^{2}}+\frac{5y^{2}y^{2}}{y^{2}}=16$$

Gan fod gan \frac{12^{2}}{y^{2}} a \frac{5y^{2}y^{2}}{y^{2}} yr un dynodydd, adiwch nhw drwy adio eu rhifiaduron.

$$\frac{12^{2}+5y^{2}y^{2}}{y^{2}}=16$$

Gwnewch y gwaith lluosi yn 12^{2}+5y^{2}y^{2}.

$$\frac{12^{2}+5y^{4}}{y^{2}}=16$$

Cyfuno termau tebyg yn 12^{2}+5y^{4}.

$$\frac{144+5y^{4}}{y^{2}}=16$$

Tynnu 16 o'r ddwy ochr.

$$\frac{144+5y^{4}}{y^{2}}-16=0$$

I ychwanegu neu dynnu mynegiannau, rhaid i chi eu ehangu i wneud eu enwaduron yr un fath. Lluoswch 16 â \frac{y^{2}}{y^{2}}.

$$\frac{144+5y^{4}}{y^{2}}-\frac{16y^{2}}{y^{2}}=0$$

Gan fod gan \frac{144+5y^{4}}{y^{2}} a \frac{16y^{2}}{y^{2}} yr un dynodydd, tynnwch nhw drwy dynnu eu rhifiaduron.

$$\frac{144+5y^{4}-16y^{2}}{y^{2}}=0$$

All y newidyn y ddim fod yn hafal i 0 gan nad ydy rhannu â sero wedi’i ddiffinio. Lluoswch ddwy ochr yr hafaliad â y^{2}.

$$144+5y^{4}-16y^{2}=0$$

Amnewid t am y^{2}.

$$5t^{2}-16t+144=0$$

Gellir datrys pob hafaliad sydd ar y ffurf ax^{2}+bx+c=0 gan ddefnyddio'r fformiwla cwadratig: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Rhowch 5 ar gyfer a, -16 ar gyfer b, a 144 ar gyfer c yn y fformiwla cwadratig.

$$t=\frac{-\left(-16\right)±\sqrt{\left(-16\right)^{2}-4\times 5\times 144}}{2\times 5}$$

Gwnewch y gwaith cyfrifo.

$$t=\frac{16±\sqrt{-2624}}{10}$$

Datryswch yr hafaliad t=\frac{16±\sqrt{-2624}}{10} pan fo ± yn plws a phan fo ± yn minws.

$$t=\frac{8+4\sqrt{41}i}{5} t=\frac{-4\sqrt{41}i+8}{5}$$

Gan fod y=t^{2}, gellir datrys yr hafaliad drwy enrhifo y=±\sqrt{t} ar gyfer pob t.

$$y=\frac{2\sqrt{3}\times 5^{\frac{3}{4}}e^{\frac{\arctan(\frac{\sqrt{41}}{2})i+2\pi i}{2}}}{5} y=\frac{2\sqrt{3}\times 5^{\frac{3}{4}}e^{\frac{\arctan(\frac{\sqrt{41}}{2})i}{2}}}{5} y=\frac{2\sqrt{3}\times 5^{\frac{3}{4}}e^{-\frac{\arctan(\frac{\sqrt{41}}{2})i}{2}}}{5} y=\frac{2\sqrt{3}\times 5^{\frac{3}{4}}e^{\frac{-\arctan(\frac{\sqrt{41}}{2})i+2\pi i}{2}}}{5}$$

All y newidyn y ddim fod yn hafal i 0.

$$y=\frac{2\sqrt{3}\times 5^{\frac{3}{4}}e^{\frac{-\arctan(\frac{\sqrt{41}}{2})i+2\pi i}{2}}}{5}\text{, }y\neq 0 y=\frac{2\sqrt{3}\times 5^{\frac{3}{4}}e^{-\frac{\arctan(\frac{\sqrt{41}}{2})i}{2}}}{5}\text{, }y\neq 0 y=\frac{2\sqrt{3}\times 5^{\frac{3}{4}}e^{\frac{\arctan(\frac{\sqrt{41}}{2})i}{2}}}{5}\text{, }y\neq 0 y=\frac{2\sqrt{3}\times 5^{\frac{3}{4}}e^{\frac{\arctan(\frac{\sqrt{41}}{2})i+2\pi i}{2}}}{5}\text{, }y\neq 0$$