Whakaoti i te (1+5sqrt{2})(1-2sqrt{2})-sqrt{18}

$$(1+5 \sqrt{ 2 } )(1-2 \sqrt{ 2 } )- \sqrt{ 18 }$$

Aromātai

$$-19$$

Ngā Upane Otinga

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o 1+5\sqrt{2} ki ia tau o 1-2\sqrt{2}.

$$1-2\sqrt{2}+5\sqrt{2}-10\left(\sqrt{2}\right)^{2}-\sqrt{18}$$

Pahekotia te -2\sqrt{2} me 5\sqrt{2}, ka 3\sqrt{2}.

$$1+3\sqrt{2}-10\left(\sqrt{2}\right)^{2}-\sqrt{18}$$

Ko te pūrua o \sqrt{2} ko 2.

$$1+3\sqrt{2}-10\times 2-\sqrt{18}$$

Whakareatia te -10 ki te 2, ka -20.

$$1+3\sqrt{2}-20-\sqrt{18}$$

Tangohia te 20 i te 1, ka -19.

$$-19+3\sqrt{2}-\sqrt{18}$$

Tauwehea te 18=3^{2}\times 2. Tuhia anō te pūtake rua o te hua \sqrt{3^{2}\times 2} hei hua o ngā pūtake rua \sqrt{3^{2}}\sqrt{2}. Tuhia te pūtakerua o te 3^{2}.

$$-19+3\sqrt{2}-3\sqrt{2}$$

Pahekotia te 3\sqrt{2} me -3\sqrt{2}, ka 0.

$$-19$$

Tauwehe

$$-19$$