Whakaoti i te a+bsqrt{2}=3(1-sqrt{2})+4sqrt{2}

$$a + b \sqrt { 2 } = 3 ( 1 - \sqrt { 2 } ) + 4 \sqrt { 2 }$$

Whakaoti mō b

$$b=-\frac{\sqrt{2}\left(a-\sqrt{2}-3\right)}{2}$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te 1-\sqrt{2}.

$$a+b\sqrt{2}=3-3\sqrt{2}+4\sqrt{2}$$

Pahekotia te -3\sqrt{2} me 4\sqrt{2}, ka \sqrt{2}.

$$a+b\sqrt{2}=3+\sqrt{2}$$

Tangohia te a mai i ngā taha e rua.

$$b\sqrt{2}=3+\sqrt{2}-a$$

He hanga arowhānui tō te whārite.

$$\sqrt{2}b=-a+\sqrt{2}+3$$

Whakawehea ngā taha e rua ki te \sqrt{2}.

$$\frac{\sqrt{2}b}{\sqrt{2}}=\frac{-a+\sqrt{2}+3}{\sqrt{2}}$$

Mā te whakawehe ki te \sqrt{2} ka wetekia te whakareanga ki te \sqrt{2}.

$$b=\frac{-a+\sqrt{2}+3}{\sqrt{2}}$$

Whakawehe 3+\sqrt{2}-a ki te \sqrt{2}.

$$b=\frac{\sqrt{2}\left(-a+\sqrt{2}+3\right)}{2}$$

Whakaoti mō a

$$a=-\sqrt{2}\left(b-1\right)+3$$