Whakaoti i te frac{2left(0.8+sqrt{2}right)}{{left(0.2sqrt{2}-0.06right)}^2}

$$\frac{ 2 \left( 0.8+ \sqrt{ 2 } \right) }{ { \left(0.2 \sqrt{ 2 } -0.06 \right) }^{ 2 } }$$

Aromātai

$$\frac{1285000\sqrt{2}+1436000}{36481}\approx 89.176953144$$

Ngā Upane Otinga

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(0.2\sqrt{2}-0.06\right)^{2}.

$$\frac{2\left(0.8+\sqrt{2}\right)}{0.04\left(\sqrt{2}\right)^{2}-0.024\sqrt{2}+0.0036}$$

Ko te pūrua o \sqrt{2} ko 2.

$$\frac{2\left(0.8+\sqrt{2}\right)}{0.04\times 2-0.024\sqrt{2}+0.0036}$$

Whakareatia te 0.04 ki te 2, ka 0.08.

$$\frac{2\left(0.8+\sqrt{2}\right)}{0.08-0.024\sqrt{2}+0.0036}$$

Tāpirihia te 0.08 ki te 0.0036, ka 0.0836.

$$\frac{2\left(0.8+\sqrt{2}\right)}{0.0836-0.024\sqrt{2}}$$

Whakangāwaritia te tauraro o \frac{2\left(0.8+\sqrt{2}\right)}{0.0836-0.024\sqrt{2}} mā te whakarea i te taurunga me te tauraro ki te 0.0836+0.024\sqrt{2}.

$$\frac{2\left(0.8+\sqrt{2}\right)\left(0.0836+0.024\sqrt{2}\right)}{\left(0.0836-0.024\sqrt{2}\right)\left(0.0836+0.024\sqrt{2}\right)}$$

Whakaarohia te \left(0.0836-0.024\sqrt{2}\right)\left(0.0836+0.024\sqrt{2}\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{2\left(0.8+\sqrt{2}\right)\left(0.0836+0.024\sqrt{2}\right)}{0.0836^{2}-\left(-0.024\sqrt{2}\right)^{2}}$$

Tātaihia te 0.0836 mā te pū o 2, kia riro ko 0.00698896.

$$\frac{2\left(0.8+\sqrt{2}\right)\left(0.0836+0.024\sqrt{2}\right)}{0.00698896-\left(-0.024\sqrt{2}\right)^{2}}$$

Whakarohaina te \left(-0.024\sqrt{2}\right)^{2}.

$$\frac{2\left(0.8+\sqrt{2}\right)\left(0.0836+0.024\sqrt{2}\right)}{0.00698896-\left(-0.024\right)^{2}\left(\sqrt{2}\right)^{2}}$$

Tātaihia te -0.024 mā te pū o 2, kia riro ko 0.000576.

$$\frac{2\left(0.8+\sqrt{2}\right)\left(0.0836+0.024\sqrt{2}\right)}{0.00698896-0.000576\left(\sqrt{2}\right)^{2}}$$

Ko te pūrua o \sqrt{2} ko 2.

$$\frac{2\left(0.8+\sqrt{2}\right)\left(0.0836+0.024\sqrt{2}\right)}{0.00698896-0.000576\times 2}$$

Whakareatia te 0.000576 ki te 2, ka 0.001152.

$$\frac{2\left(0.8+\sqrt{2}\right)\left(0.0836+0.024\sqrt{2}\right)}{0.00698896-0.001152}$$

Tangohia te 0.001152 i te 0.00698896, ka 0.00583696.

$$\frac{2\left(0.8+\sqrt{2}\right)\left(0.0836+0.024\sqrt{2}\right)}{0.00583696}$$

Whakawehea te 2\left(0.8+\sqrt{2}\right)\left(0.0836+0.024\sqrt{2}\right) ki te 0.00583696, kia riro ko \frac{12500000}{36481}\left(0.8+\sqrt{2}\right)\left(0.0836+0.024\sqrt{2}\right).

$$\frac{12500000}{36481}\left(0.8+\sqrt{2}\right)\left(0.0836+0.024\sqrt{2}\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{12500000}{36481} ki te 0.8+\sqrt{2}.

$$\left(\frac{10000000}{36481}+\frac{12500000}{36481}\sqrt{2}\right)\left(0.0836+0.024\sqrt{2}\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te \frac{10000000}{36481}+\frac{12500000}{36481}\sqrt{2} ki te 0.0836+0.024\sqrt{2} ka whakakotahi i ngā kupu rite.

$$\frac{836000}{36481}+\frac{1285000}{36481}\sqrt{2}+\frac{300000}{36481}\left(\sqrt{2}\right)^{2}$$

Ko te pūrua o \sqrt{2} ko 2.

$$\frac{836000}{36481}+\frac{1285000}{36481}\sqrt{2}+\frac{300000}{36481}\times 2$$

Whakareatia te \frac{300000}{36481} ki te 2, ka \frac{600000}{36481}.

$$\frac{836000}{36481}+\frac{1285000}{36481}\sqrt{2}+\frac{600000}{36481}$$

Tāpirihia te \frac{836000}{36481} ki te \frac{600000}{36481}, ka \frac{1436000}{36481}.

$$\frac{1436000}{36481}+\frac{1285000}{36481}\sqrt{2}$$