Whakaoti i te (x-frac{sqrt{3}+1}{2})=frac{-4sqrt{3}+(sqrt{3}+1)^2}{4}

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

Whakaoti mō x

$$x = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

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.

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

Whakamahia te āhuatanga tohatoha hei whakarea te -2 ki te \sqrt{3}+1.

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

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(\sqrt{3}+1\right)^{2}.

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

Ko te pūrua o \sqrt{3} ko 3.

$$4x-2\sqrt{3}-2=-4\sqrt{3}+3+2\sqrt{3}+1$$

Tāpirihia te 3 ki te 1, ka 4.

$$4x-2\sqrt{3}-2=-4\sqrt{3}+4+2\sqrt{3}$$

Pahekotia te -4\sqrt{3} me 2\sqrt{3}, ka -2\sqrt{3}.

$$4x-2\sqrt{3}-2=-2\sqrt{3}+4$$

Me tāpiri te 2\sqrt{3} ki ngā taha e rua.

$$4x-2=-2\sqrt{3}+4+2\sqrt{3}$$

Pahekotia te -2\sqrt{3} me 2\sqrt{3}, ka 0.

$$4x-2=4$$

Me tāpiri te 2 ki ngā taha e rua.

$$4x=4+2$$

Tāpirihia te 4 ki te 2, ka 6.

$$4x=6$$

Whakawehea ngā taha e rua ki te 4.

$$x=\frac{6}{4}$$

Whakahekea te hautanga \frac{6}{4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x=\frac{3}{2}$$