Whakaoti i te (4)(sqrt{2}+2sqrt{3})(sqrt{2}-2sqrt{3})+(2sqrt{3})^2

$$( 4 ) ( \sqrt { 2 } + 2 \sqrt { 3 } ) ( \sqrt { 2 } - 2 \sqrt { 3 } ) + ( 2 \sqrt { 3 } ) ^ { 2 }$$

Aromātai

$$-28$$

Ngā Upane Otinga

Whakamahia te āhuatanga tohatoha hei whakarea te 4 ki te \sqrt{2}+2\sqrt{3}.

$$\left(4\sqrt{2}+8\sqrt{3}\right)\left(\sqrt{2}-2\sqrt{3}\right)+\left(2\sqrt{3}\right)^{2}$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 4\sqrt{2}+8\sqrt{3} ki te \sqrt{2}-2\sqrt{3} ka whakakotahi i ngā kupu rite.

$$4\left(\sqrt{2}\right)^{2}-16\left(\sqrt{3}\right)^{2}+\left(2\sqrt{3}\right)^{2}$$

Ko te pūrua o \sqrt{2} ko 2.

$$4\times 2-16\left(\sqrt{3}\right)^{2}+\left(2\sqrt{3}\right)^{2}$$

Whakareatia te 4 ki te 2, ka 8.

$$8-16\left(\sqrt{3}\right)^{2}+\left(2\sqrt{3}\right)^{2}$$

Ko te pūrua o \sqrt{3} ko 3.

$$8-16\times 3+\left(2\sqrt{3}\right)^{2}$$

Whakareatia te -16 ki te 3, ka -48.

$$8-48+\left(2\sqrt{3}\right)^{2}$$

Tangohia te 48 i te 8, ka -40.

$$-40+\left(2\sqrt{3}\right)^{2}$$

Whakarohaina te \left(2\sqrt{3}\right)^{2}.

$$-40+2^{2}\left(\sqrt{3}\right)^{2}$$

Tātaihia te 2 mā te pū o 2, kia riro ko 4.

$$-40+4\left(\sqrt{3}\right)^{2}$$

Ko te pūrua o \sqrt{3} ko 3.

$$-40+4\times 3$$

Whakareatia te 4 ki te 3, ka 12.

$$-40+12$$

Tāpirihia te -40 ki te 12, ka -28.

$$-28$$

Tauwehe

$$-28$$