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

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

Aromātai

$$-6\sqrt{6}-6\approx -20.696938457$$

Ngā Upane Otinga

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o 3\sqrt{2}+2\sqrt{3} ki ia tau o 3\sqrt{2}-4\sqrt{3}.

$$9\left(\sqrt{2}\right)^{2}-12\sqrt{3}\sqrt{2}+6\sqrt{3}\sqrt{2}-8\left(\sqrt{3}\right)^{2}$$

Ko te pūrua o \sqrt{2} ko 2.

$$9\times 2-12\sqrt{3}\sqrt{2}+6\sqrt{3}\sqrt{2}-8\left(\sqrt{3}\right)^{2}$$

Whakareatia te 9 ki te 2, ka 18.

$$18-12\sqrt{3}\sqrt{2}+6\sqrt{3}\sqrt{2}-8\left(\sqrt{3}\right)^{2}$$

Hei whakarea \sqrt{3} me \sqrt{2}, whakareatia ngā tau i raro i te pūtake rua.

$$18-12\sqrt{6}+6\sqrt{3}\sqrt{2}-8\left(\sqrt{3}\right)^{2}$$

Hei whakarea \sqrt{3} me \sqrt{2}, whakareatia ngā tau i raro i te pūtake rua.

$$18-12\sqrt{6}+6\sqrt{6}-8\left(\sqrt{3}\right)^{2}$$

Pahekotia te -12\sqrt{6} me 6\sqrt{6}, ka -6\sqrt{6}.

$$18-6\sqrt{6}-8\left(\sqrt{3}\right)^{2}$$

Ko te pūrua o \sqrt{3} ko 3.

$$18-6\sqrt{6}-8\times 3$$

Whakareatia te -8 ki te 3, ka -24.

$$18-6\sqrt{6}-24$$

Tangohia te 24 i te 18, ka -6.

$$-6-6\sqrt{6}$$

Tauwehe

$$6 {(-\sqrt{6} - 1)} = -20.696938457$$