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

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

Whakaoti mō x

$$x=-\frac{1}{12}\approx -0.083333333$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(x+2\right)^{2}.

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

Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te x-1.

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

Whakamahia te āhuatanga tuaritanga hei whakarea te 3x-3 ki te x+1 ka whakakotahi i ngā kupu rite.

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

Pahekotia te x^{2} me 3x^{2}, ka 4x^{2}.

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

Tangohia te 3 i te 4, ka 1.

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

Whakamahia te āhuatanga tohatoha hei whakarea te 4x ki te x-2.

$$4x^{2}+4x+1=4x^{2}-8x$$

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

$$4x^{2}+4x+1-4x^{2}=-8x$$

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

$$4x+1=-8x$$

Me tāpiri te 8x ki ngā taha e rua.

$$4x+1+8x=0$$

Pahekotia te 4x me 8x, ka 12x.

$$12x+1=0$$

Tangohia te 1 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$12x=-1$$

Whakawehea ngā taha e rua ki te 12.

$$x=\frac{-1}{12}$$

Ka taea te hautanga \frac{-1}{12} te tuhi anō ko -\frac{1}{12} mā te tango i te tohu tōraro.

$$x=-\frac{1}{12}$$