Whakaoti i te (4)(sqrt{3}-sqrt{5})(sqrt{5}+sqrt{3})=

$$( 4 ) ( \sqrt { 3 } - \sqrt { 5 } ) ( \sqrt { 5 } + \sqrt { 3 } ) =$$

Aromātai

$$-8$$

Ngā Upane Otinga

Whakamahia te āhuatanga tohatoha hei whakarea te 4 ki te \sqrt{3}-\sqrt{5}.

$$\left(4\sqrt{3}-4\sqrt{5}\right)\left(\sqrt{5}+\sqrt{3}\right)$$

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o 4\sqrt{3}-4\sqrt{5} ki ia tau o \sqrt{5}+\sqrt{3}.

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

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

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

Ko te pūrua o \sqrt{3} ko 3.

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

Whakareatia te 4 ki te 3, ka 12.

$$4\sqrt{15}+12-4\left(\sqrt{5}\right)^{2}-4\sqrt{5}\sqrt{3}$$

Ko te pūrua o \sqrt{5} ko 5.

$$4\sqrt{15}+12-4\times 5-4\sqrt{5}\sqrt{3}$$

Whakareatia te -4 ki te 5, ka -20.

$$4\sqrt{15}+12-20-4\sqrt{5}\sqrt{3}$$

Tangohia te 20 i te 12, ka -8.

$$4\sqrt{15}-8-4\sqrt{5}\sqrt{3}$$

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

$$4\sqrt{15}-8-4\sqrt{15}$$

Pahekotia te 4\sqrt{15} me -4\sqrt{15}, ka 0.

$$-8$$

Tauwehe

$$-8$$