Whakaoti i te (5sqrt{2}-e)(3sqrt{2}+e)=fsqrt{2}-6

$$( 5 \sqrt { 2 } - e ) ( 3 \sqrt { 2 } + e ) = f \sqrt { 2 } - 6$$

Whakaoti mō f

$$f=-\frac{\sqrt{2}e^{2}}{2}+2e+18\sqrt{2}\approx 25.667556106$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o 5\sqrt{2}-e ki ia tau o 3\sqrt{2}+e.

$$15\left(\sqrt{2}\right)^{2}+5\sqrt{2}e-3e\sqrt{2}-e^{2}=f\sqrt{2}-6$$

Ko te pūrua o \sqrt{2} ko 2.

$$15\times 2+5\sqrt{2}e-3e\sqrt{2}-e^{2}=f\sqrt{2}-6$$

Whakareatia te 15 ki te 2, ka 30.

$$30+5\sqrt{2}e-3e\sqrt{2}-e^{2}=f\sqrt{2}-6$$

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

$$30+2\sqrt{2}e-e^{2}=f\sqrt{2}-6$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$f\sqrt{2}-6=30+2\sqrt{2}e-e^{2}$$

Me tāpiri te 6 ki ngā taha e rua.

$$f\sqrt{2}=30+2\sqrt{2}e-e^{2}+6$$

Tāpirihia te 30 ki te 6, ka 36.

$$f\sqrt{2}=36+2\sqrt{2}e-e^{2}$$

He hanga arowhānui tō te whārite.

$$\sqrt{2}f=2e\sqrt{2}-e^{2}+36$$

Whakawehea ngā taha e rua ki te \sqrt{2}.

$$\frac{\sqrt{2}f}{\sqrt{2}}=\frac{2e\sqrt{2}-e^{2}+36}{\sqrt{2}}$$

Mā te whakawehe ki te \sqrt{2} ka wetekia te whakareanga ki te \sqrt{2}.

$$f=\frac{2e\sqrt{2}-e^{2}+36}{\sqrt{2}}$$

Whakawehe 36+2e\sqrt{2}-e^{2} ki te \sqrt{2}.

$$f=\frac{\sqrt{2}\left(2e\sqrt{2}-e^{2}+36\right)}{2}$$