Whakaoti i te (2x-3)^2-5=0

$$( 2 x - 3 ) ^ { 2 } - 5 = 0$$

Whakaoti mō x

$$x = \frac{\sqrt{5} + 3}{2} \approx 2.618033989$$

$$x=\frac{3-\sqrt{5}}{2}\approx 0.381966011$$

Ngā Upane mā te Kimi Pūtakerua

Me tāpiri 5 ki ngā taha e rua o te whārite.

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

Mā te tango i te 5 i a ia ake anō ka toe ko te 0.

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

Tuhia te pūtakerua o ngā taha e rua o te whārite.

$$2x-3=\sqrt{5} 2x-3=-\sqrt{5}$$

Me tāpiri 3 ki ngā taha e rua o te whārite.

$$2x-3-\left(-3\right)=\sqrt{5}-\left(-3\right) 2x-3-\left(-3\right)=-\sqrt{5}-\left(-3\right)$$

Mā te tango i te -3 i a ia ake anō ka toe ko te 0.

$$2x=\sqrt{5}-\left(-3\right) 2x=-\sqrt{5}-\left(-3\right)$$

Tango -3 mai i \sqrt{5}.

$$2x=\sqrt{5}+3$$

Tango -3 mai i -\sqrt{5}.

$$2x=3-\sqrt{5}$$

Whakawehea ngā taha e rua ki te 2.

$$\frac{2x}{2}=\frac{\sqrt{5}+3}{2} \frac{2x}{2}=\frac{3-\sqrt{5}}{2}$$

Mā te whakawehe ki te 2 ka wetekia te whakareanga ki te 2.

$$x=\frac{\sqrt{5}+3}{2} x=\frac{3-\sqrt{5}}{2}$$