Whakaoti i te sqrt{2}(x-1)=2(x-2)+3sqrt{2}

$$\sqrt { 2 } ( x - 1 ) = 2 ( x - 2 ) + 3 \sqrt { 2 }$$

Whakaoti mō x

$$x=-2\sqrt{2}\approx -2.828427125$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$\sqrt{2}x-\sqrt{2}=2\left(x-2\right)+3\sqrt{2}$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2 ki te x-2.

$$\sqrt{2}x-\sqrt{2}=2x-4+3\sqrt{2}$$

Tangohia te 2x mai i ngā taha e rua.

$$\sqrt{2}x-\sqrt{2}-2x=-4+3\sqrt{2}$$

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

$$\sqrt{2}x-2x=-4+3\sqrt{2}+\sqrt{2}$$

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

$$\sqrt{2}x-2x=-4+4\sqrt{2}$$

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

$$\left(\sqrt{2}-2\right)x=-4+4\sqrt{2}$$

He hanga arowhānui tō te whārite.

$$\left(\sqrt{2}-2\right)x=4\sqrt{2}-4$$

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

$$\frac{\left(\sqrt{2}-2\right)x}{\sqrt{2}-2}=\frac{4\sqrt{2}-4}{\sqrt{2}-2}$$

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

$$x=\frac{4\sqrt{2}-4}{\sqrt{2}-2}$$

Whakawehe -4+4\sqrt{2} ki te \sqrt{2}-2.

$$x=-2\sqrt{2}$$