Whakaoti i te sqrt{98}:(x+4)(2x-3)=6

$$\sqrt { 98 } : ( x + 4 ) ( 2 x - 3 ) = 6$$

Whakaoti mō x

$$x=\frac{231\sqrt{2}}{178}+\frac{183}{89}\approx 3.891479398$$

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.

$$\sqrt{98}\left(2x-3\right)=6\left(x+4\right)$$

Tauwehea te 98=7^{2}\times 2. Tuhia anō te pūtake rua o te hua \sqrt{7^{2}\times 2} hei hua o ngā pūtake rua \sqrt{7^{2}}\sqrt{2}. Tuhia te pūtakerua o te 7^{2}.

$$7\sqrt{2}\left(2x-3\right)=6\left(x+4\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 7\sqrt{2} ki te 2x-3.

$$14x\sqrt{2}-21\sqrt{2}=6\left(x+4\right)$$

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

$$14x\sqrt{2}-21\sqrt{2}=6x+24$$

Tangohia te 6x mai i ngā taha e rua.

$$14x\sqrt{2}-21\sqrt{2}-6x=24$$

Me tāpiri te 21\sqrt{2} ki ngā taha e rua.

$$14x\sqrt{2}-6x=24+21\sqrt{2}$$

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

$$\left(14\sqrt{2}-6\right)x=24+21\sqrt{2}$$

He hanga arowhānui tō te whārite.

$$\left(14\sqrt{2}-6\right)x=21\sqrt{2}+24$$

Whakawehea ngā taha e rua ki te 14\sqrt{2}-6.

$$\frac{\left(14\sqrt{2}-6\right)x}{14\sqrt{2}-6}=\frac{21\sqrt{2}+24}{14\sqrt{2}-6}$$

Mā te whakawehe ki te 14\sqrt{2}-6 ka wetekia te whakareanga ki te 14\sqrt{2}-6.

$$x=\frac{21\sqrt{2}+24}{14\sqrt{2}-6}$$

Whakawehe 24+21\sqrt{2} ki te 14\sqrt{2}-6.

$$x=\frac{231\sqrt{2}}{178}+\frac{183}{89}$$