Whakaoti i te sqrt[8]{8}:(x+4)(2x-3)=6

$$\sqrt[ 8 ] { 8 } : ( x + 4 ) ( 2 x - 3 ) = 6$$

Whakaoti mō x

$$x = -\frac{3 \cdot 2 ^ {\frac{3}{8}} {(2 \sqrt{2} + 81)} {(4 \cdot 2 ^ {\frac{5}{8}} + 1)} {(2 ^ {\frac{3}{8}} + 3)} {(2 ^ {\frac{3}{4}} + 9)}}{13106} \approx -8.187871771$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe x ki -4 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x+4.

$$\sqrt[8]{8}\left(2x-3\right)=6\left(x+4\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te \sqrt[8]{8} ki te 2x-3.

$$2\sqrt[8]{8}x-3\sqrt[8]{8}=6\left(x+4\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 6 ki te x+4.

$$2\sqrt[8]{8}x-3\sqrt[8]{8}=6x+24$$

Tangohia te 6x mai i ngā taha e rua.

$$2\sqrt[8]{8}x-3\sqrt[8]{8}-6x=24$$

Me tāpiri te 3\sqrt[8]{8} ki ngā taha e rua.

$$2\sqrt[8]{8}x-6x=24+3\sqrt[8]{8}$$

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

$$\left(2\sqrt[8]{8}-6\right)x=24+3\sqrt[8]{8}$$

He hanga arowhānui tō te whārite.

$$\left(2\sqrt[8]{8}-6\right)x=3\sqrt[8]{8}+24$$

Whakawehea ngā taha e rua ki te 2\sqrt[8]{8}-6.

$$\frac{\left(2\sqrt[8]{8}-6\right)x}{2\sqrt[8]{8}-6}=\frac{3\times 2^{\frac{3}{8}}+24}{2\sqrt[8]{8}-6}$$

Mā te whakawehe ki te 2\sqrt[8]{8}-6 ka wetekia te whakareanga ki te 2\sqrt[8]{8}-6.

$$x=\frac{3\times 2^{\frac{3}{8}}+24}{2\sqrt[8]{8}-6}$$

Whakawehe 24+3\times 2^{\frac{3}{8}} ki te 2\sqrt[8]{8}-6.

$$x=-\frac{3\left(2\sqrt{2}+81\right)\left(2^{\frac{3}{8}}+3\right)\left(2^{\frac{3}{4}}+9\right)\left(2^{\frac{7}{8}}+1\right)\sqrt[8]{2}\left(\sqrt[4]{2}+4-2\sqrt[8]{2}\right)}{13106}$$