Whakaoti i te x/2(x^3-1)+(5x^2-1/4)(x-3)+3x^2=x^2(1/2x-1/4)(x+3)

$$\frac { x } { 2 } ( x ^ { 3 } - 1 ) + ( \frac { 5 x ^ { 2 } - 1 } { 4 } ) ( x - 3 ) + 3 x ^ { 2 } = x ^ { 2 } ( \frac { 1 } { 2 } x - \frac { 1 } { 4 } ) ( x + 3 )$$

Whakaoti mō x

$$x=1$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te 4, arā, te tauraro pātahi he tino iti rawa te kitea o 2,4.

$$2x\left(x^{3}-1\right)+\left(5x^{2}-1\right)\left(x-3\right)+12x^{2}=4x^{2}\left(\frac{1}{2}x-\frac{1}{4}\right)\left(x+3\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2x ki te x^{3}-1.

$$2x^{4}-2x+\left(5x^{2}-1\right)\left(x-3\right)+12x^{2}=4x^{2}\left(\frac{1}{2}x-\frac{1}{4}\right)\left(x+3\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 5x^{2}-1 ki te x-3.

$$2x^{4}-2x+5x^{3}-15x^{2}-x+3+12x^{2}=4x^{2}\left(\frac{1}{2}x-\frac{1}{4}\right)\left(x+3\right)$$

Pahekotia te -2x me -x, ka -3x.

$$2x^{4}-3x+5x^{3}-15x^{2}+3+12x^{2}=4x^{2}\left(\frac{1}{2}x-\frac{1}{4}\right)\left(x+3\right)$$

Pahekotia te -15x^{2} me 12x^{2}, ka -3x^{2}.

$$2x^{4}-3x+5x^{3}-3x^{2}+3=4x^{2}\left(\frac{1}{2}x-\frac{1}{4}\right)\left(x+3\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 4x^{2} ki te \frac{1}{2}x-\frac{1}{4}.

$$2x^{4}-3x+5x^{3}-3x^{2}+3=\left(2x^{3}-x^{2}\right)\left(x+3\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 2x^{3}-x^{2} ki te x+3 ka whakakotahi i ngā kupu rite.

$$2x^{4}-3x+5x^{3}-3x^{2}+3=2x^{4}+5x^{3}-3x^{2}$$

Tangohia te 2x^{4} mai i ngā taha e rua.

$$2x^{4}-3x+5x^{3}-3x^{2}+3-2x^{4}=5x^{3}-3x^{2}$$

Pahekotia te 2x^{4} me -2x^{4}, ka 0.

$$-3x+5x^{3}-3x^{2}+3=5x^{3}-3x^{2}$$

Tangohia te 5x^{3} mai i ngā taha e rua.

$$-3x+5x^{3}-3x^{2}+3-5x^{3}=-3x^{2}$$

Pahekotia te 5x^{3} me -5x^{3}, ka 0.

$$-3x-3x^{2}+3=-3x^{2}$$

Me tāpiri te 3x^{2} ki ngā taha e rua.

$$-3x-3x^{2}+3+3x^{2}=0$$

Pahekotia te -3x^{2} me 3x^{2}, ka 0.

$$-3x+3=0$$

Tangohia te 3 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-3x=-3$$

Whakawehea ngā taha e rua ki te -3.

$$x=\frac{-3}{-3}$$

Whakawehea te -3 ki te -3, kia riro ko 1.

$$x=1$$