Whakaoti i te operatorname{gcd}(9872)=98x+72y*9

$$\operatorname { gcd } ( 9872 ) = 98 x + 72 y \cdot 9$$

Whakaoti mō c

$$\left\{\begin{matrix}c=\frac{49x+324y}{4936dg}\text{, }&d\neq 0\text{ and }g\neq 0\\c\in \mathrm{R}\text{, }&x=-\frac{324y}{49}\text{ and }\left(d=0\text{ or }g=0\right)\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakareatia te 72 ki te 9, ka 648.

$$gcd\times 9872=98x+648y$$

He hanga arowhānui tō te whārite.

$$9872dgc=98x+648y$$

Whakawehea ngā taha e rua ki te 9872gd.

$$\frac{9872dgc}{9872dg}=\frac{98x+648y}{9872dg}$$

Mā te whakawehe ki te 9872gd ka wetekia te whakareanga ki te 9872gd.

$$c=\frac{98x+648y}{9872dg}$$

Whakawehe 98x+648y ki te 9872gd.

$$c=\frac{49x+324y}{4936dg}$$

Whakaoti mō d

$$\left\{\begin{matrix}d=\frac{49x+324y}{4936cg}\text{, }&c\neq 0\text{ and }g\neq 0\\d\in \mathrm{R}\text{, }&x=-\frac{324y}{49}\text{ and }\left(c=0\text{ or }g=0\right)\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakareatia te 72 ki te 9, ka 648.

$$gcd\times 9872=98x+648y$$

He hanga arowhānui tō te whārite.

$$9872cgd=98x+648y$$

Whakawehea ngā taha e rua ki te 9872gc.

$$\frac{9872cgd}{9872cg}=\frac{98x+648y}{9872cg}$$

Mā te whakawehe ki te 9872gc ka wetekia te whakareanga ki te 9872gc.

$$d=\frac{98x+648y}{9872cg}$$

Whakawehe 98x+648y ki te 9872gc.

$$d=\frac{49x+324y}{4936cg}$$