Whakaoti i te (-1/2-a)(1/2-a)(a^2+1/4)+(1-a^2)(a^2+1)

$$( - \frac { 1 } { 2 } - a ) ( \frac { 1 } { 2 } - a ) ( a ^ { 2 } + \frac { 1 } { 4 } ) + ( 1 - a ^ { 2 } ) ( a ^ { 2 } + 1 )$$

Aromātai

$$\frac{15}{16}=0.9375$$

Ngā Upane Otinga

Whakamahia te āhuatanga tuaritanga hei whakarea te -\frac{1}{2}-a ki te \frac{1}{2}-a ka whakakotahi i ngā kupu rite.

$$\left(-\frac{1}{4}+a^{2}\right)\left(a^{2}+\frac{1}{4}\right)+\left(1-a^{2}\right)\left(a^{2}+1\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te -\frac{1}{4}+a^{2} ki te a^{2}+\frac{1}{4} ka whakakotahi i ngā kupu rite.

$$-\frac{1}{16}+a^{4}+\left(1-a^{2}\right)\left(a^{2}+1\right)$$

Whakaarohia te \left(1-a^{2}\right)\left(a^{2}+1\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}. Pūrua 1.

$$-\frac{1}{16}+a^{4}+1-\left(a^{2}\right)^{2}$$

Hei hiki pū ki tētahi pū anō, me whakarea ngā taupū. Me whakarea te 2 me te 2 kia riro ai te 4.

$$-\frac{1}{16}+a^{4}+1-a^{4}$$

Tāpirihia te -\frac{1}{16} ki te 1, ka \frac{15}{16}.

$$\frac{15}{16}+a^{4}-a^{4}$$

Pahekotia te a^{4} me -a^{4}, ka 0.

$$\frac{15}{16}$$

Tauwehe

$$\frac{3 \cdot 5}{2 ^ {4}} = 0.9375$$

Ngā Upane Otinga

Tauwehea te \frac{1}{16}.

$$\frac{\left(-1-2a\right)\left(1-2a\right)\left(4a^{2}+1\right)+16\left(1-a^{2}\right)\left(a^{2}+1\right)}{16}$$

Whakarūnātia.

$$\frac{15}{16}$$