Whakaoti i te [1/2(sqrt{5}+sqrt{3})]^2

$$[ \frac { 1 } { 2 } ( \sqrt { 5 } + \sqrt { 3 } ) ] ^ { 2 }$$

Aromātai

$$\frac{\sqrt{15}}{2}+2\approx 3.936491673$$

Ngā Upane Otinga

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{1}{2} ki te \sqrt{5}+\sqrt{3}.

$$\left(\frac{1}{2}\sqrt{5}+\frac{1}{2}\sqrt{3}\right)^{2}$$

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(\frac{1}{2}\sqrt{5}+\frac{1}{2}\sqrt{3}\right)^{2}.

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

Ko te pūrua o \sqrt{5} ko 5.

$$\frac{1}{4}\times 5+\frac{1}{2}\sqrt{5}\sqrt{3}+\frac{1}{4}\left(\sqrt{3}\right)^{2}$$

Whakareatia te \frac{1}{4} ki te 5, ka \frac{5}{4}.

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

Hei whakarea \sqrt{5} me \sqrt{3}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{5}{4}+\frac{1}{2}\sqrt{15}+\frac{1}{4}\left(\sqrt{3}\right)^{2}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{5}{4}+\frac{1}{2}\sqrt{15}+\frac{1}{4}\times 3$$

Whakareatia te \frac{1}{4} ki te 3, ka \frac{3}{4}.

$$\frac{5}{4}+\frac{1}{2}\sqrt{15}+\frac{3}{4}$$

Tāpirihia te \frac{5}{4} ki te \frac{3}{4}, ka 2.

$$2+\frac{1}{2}\sqrt{15}$$

Whakaroha

$$\frac{\sqrt{15}}{2} + 2 = 3.936491673$$

Ngā Upane Otinga

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{1}{2} ki te \sqrt{5}+\sqrt{3}.

$$\left(\frac{1}{2}\sqrt{5}+\frac{1}{2}\sqrt{3}\right)^{2}$$

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(\frac{1}{2}\sqrt{5}+\frac{1}{2}\sqrt{3}\right)^{2}.

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

Ko te pūrua o \sqrt{5} ko 5.

$$\frac{1}{4}\times 5+\frac{1}{2}\sqrt{5}\sqrt{3}+\frac{1}{4}\left(\sqrt{3}\right)^{2}$$

Whakareatia te \frac{1}{4} ki te 5, ka \frac{5}{4}.

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

Hei whakarea \sqrt{5} me \sqrt{3}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{5}{4}+\frac{1}{2}\sqrt{15}+\frac{1}{4}\left(\sqrt{3}\right)^{2}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{5}{4}+\frac{1}{2}\sqrt{15}+\frac{1}{4}\times 3$$

Whakareatia te \frac{1}{4} ki te 3, ka \frac{3}{4}.

$$\frac{5}{4}+\frac{1}{2}\sqrt{15}+\frac{3}{4}$$

Tāpirihia te \frac{5}{4} ki te \frac{3}{4}, ka 2.

$$2+\frac{1}{2}\sqrt{15}$$