Whakaoti i te 76/a=left(15-hright)^3+k

$$\frac{ 76 }{ a } = { \left(15-h \right) }^{ 3 } +k$$

Whakaoti mō a

$$a=\frac{76}{\left(15-h\right)^{3}+k}$$

$$h\neq \sqrt[3]{k}+15$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe a ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te a.

$$76=a\left(15-h\right)^{3}+ak$$

Whakamahia te ture huarua \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} hei whakaroha \left(15-h\right)^{3}.

$$76=a\left(3375-675h+45h^{2}-h^{3}\right)+ak$$

Whakamahia te āhuatanga tohatoha hei whakarea te a ki te 3375-675h+45h^{2}-h^{3}.

$$76=3375a-675ah+45ah^{2}-ah^{3}+ak$$

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

$$3375a-675ah+45ah^{2}-ah^{3}+ak=76$$

Pahekotia ngā kīanga tau katoa e whai ana i te a.

$$\left(3375-675h+45h^{2}-h^{3}+k\right)a=76$$

He hanga arowhānui tō te whārite.

$$\left(3375+k-675h+45h^{2}-h^{3}\right)a=76$$

Whakawehea ngā taha e rua ki te 3375-675h+45h^{2}-h^{3}+k.

$$\frac{\left(3375+k-675h+45h^{2}-h^{3}\right)a}{3375+k-675h+45h^{2}-h^{3}}=\frac{76}{3375+k-675h+45h^{2}-h^{3}}$$

Mā te whakawehe ki te 3375-675h+45h^{2}-h^{3}+k ka wetekia te whakareanga ki te 3375-675h+45h^{2}-h^{3}+k.

$$a=\frac{76}{3375+k-675h+45h^{2}-h^{3}}$$

Tē taea kia ōrite te tāupe a ki 0.

$$a=\frac{76}{3375+k-675h+45h^{2}-h^{3}}\text{, }a\neq 0$$

Whakaoti mō h

$$h=-\sqrt[3]{-k+\frac{76}{a}}+15$$

$$a\neq 0$$