Whakaoti i te (1-x)^2/2-(x-1)/3<2+x^2/2

$$\frac { ( 1 - x ) ^ { 2 } } { 2 } - \frac { ( x - 1 ) } { 3 } < 2 + \frac { x ^ { 2 } } { 2 }$$

Whakaoti mō x

$$x>-\frac{7}{8}$$

Ngā Upane Otinga

Me whakarea ngā taha e rua o te whārite ki te 6, arā, te tauraro pātahi he tino iti rawa te kitea o 2,3. I te mea he tōrunga te 6, kāore e huri te ahunga koreōrite.

$$3\left(1-x\right)^{2}-2\left(x-1\right)<12+3x^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(1-x\right)^{2}.

$$3\left(1-2x+x^{2}\right)-2\left(x-1\right)<12+3x^{2}$$

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

$$3-6x+3x^{2}-2\left(x-1\right)<12+3x^{2}$$

Whakamahia te āhuatanga tohatoha hei whakarea te -2 ki te x-1.

$$3-6x+3x^{2}-2x+2<12+3x^{2}$$

Pahekotia te -6x me -2x, ka -8x.

$$3-8x+3x^{2}+2<12+3x^{2}$$

Tāpirihia te 3 ki te 2, ka 5.

$$5-8x+3x^{2}<12+3x^{2}$$

Tangohia te 3x^{2} mai i ngā taha e rua.

$$5-8x+3x^{2}-3x^{2}<12$$

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

$$5-8x<12$$

Tangohia te 5 mai i ngā taha e rua.

$$-8x<12-5$$

Tangohia te 5 i te 12, ka 7.

$$-8x<7$$

Whakawehea ngā taha e rua ki te -8. I te mea he tōraro a -8, ka huri te ahunga koreōrite.

$$x>-\frac{7}{8}$$