Datrys {l}{a^2+b^2=100}{a+b=20}

$$\left\{ \begin{array} { l } { a ^ { 2 } + b ^ { 2 } = 100 } \\ { a + b = 20 } \end{array} \right.$$

Datrys ar gyfer a, b

$$a=10+5\sqrt{2}i\approx 10+7.071067812i\text{, }b=-5\sqrt{2}i+10\approx 10-7.071067812i$$

$$a=-5\sqrt{2}i+10\approx 10-7.071067812i\text{, }b=10+5\sqrt{2}i\approx 10+7.071067812i$$

Camau gan Ddefnyddio Amnewidiad a Fformiwla Cwadratig

Datryswch a+b=20 am a drwy ynysu a ar ochr chwith yr arwydd hafal.

$$a+b=20$$

Tynnu b o ddwy ochr yr hafaliad.

$$a=-b+20$$

Amnewid -b+20 am a yn yr hafaliad arall, b^{2}+a^{2}=100.

$$b^{2}+\left(-b+20\right)^{2}=100$$

Sgwâr -b+20.

$$b^{2}+b^{2}-40b+400=100$$

Adio b^{2} at b^{2}.

$$2b^{2}-40b+400=100$$

Tynnu 100 o ddwy ochr yr hafaliad.

$$2b^{2}-40b+300=0$$

Mae’r hafaliad hwn yn y ffurf safonol: ax^{2}+bx+c=0. Amnewidiwch 1+1\left(-1\right)^{2} am a, 1\times 20\left(-1\right)\times 2 am b, a 300 am c yn y fformiwla gwadratig, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{-\left(-40\right)±\sqrt{\left(-40\right)^{2}-4\times 2\times 300}}{2\times 2}$$

Sgwâr 1\times 20\left(-1\right)\times 2.

$$b=\frac{-\left(-40\right)±\sqrt{1600-4\times 2\times 300}}{2\times 2}$$

Lluoswch -4 â 1+1\left(-1\right)^{2}.

$$b=\frac{-\left(-40\right)±\sqrt{1600-8\times 300}}{2\times 2}$$

Lluoswch -8 â 300.

$$b=\frac{-\left(-40\right)±\sqrt{1600-2400}}{2\times 2}$$

Adio 1600 at -2400.

$$b=\frac{-\left(-40\right)±\sqrt{-800}}{2\times 2}$$

Cymryd isradd -800.

$$b=\frac{-\left(-40\right)±20\sqrt{2}i}{2\times 2}$$

Gwrthwyneb 1\times 20\left(-1\right)\times 2 yw 40.

$$b=\frac{40±20\sqrt{2}i}{2\times 2}$$

Lluoswch 2 â 1+1\left(-1\right)^{2}.

$$b=\frac{40±20\sqrt{2}i}{4}$$

Datryswch yr hafaliad b=\frac{40±20\sqrt{2}i}{4} pan fydd ± yn plws. Adio 40 at 20i\sqrt{2}.

$$b=\frac{40+20\sqrt{2}i}{4}$$

Rhannwch 40+20i\sqrt{2} â 4.

$$b=10+5\sqrt{2}i$$

Datryswch yr hafaliad b=\frac{40±20\sqrt{2}i}{4} pan fydd ± yn minws. Tynnu 20i\sqrt{2} o 40.

$$b=\frac{-20\sqrt{2}i+40}{4}$$

Rhannwch 40-20i\sqrt{2} â 4.

$$b=-5\sqrt{2}i+10$$

Mae dau ateb ar gyfer b: 10+5i\sqrt{2} a 10-5i\sqrt{2}. Amnewidiwch 10+5i\sqrt{2} am b yn yr hafaliad a=-b+20 i ddod o hyd i'r ateb cyfatebol ar gyfer a sy'n bodloni'r ddau hafaliad.

$$a=-\left(10+5\sqrt{2}i\right)+20$$

Nawr, amnewidiwch 10-5i\sqrt{2} am b yn yr hafaliad a=-b+20 a’i ddatrys i ganfod yr ateb cyfatebol ar gyfer a sy'n bodloni'r ddau hafaliad.

$$a=-\left(-5\sqrt{2}i+10\right)+20$$

Mae’r system wedi’i datrys nawr.

$$a=-\left(10+5\sqrt{2}i\right)+20,b=10+5\sqrt{2}i\text{ or }a=-\left(-5\sqrt{2}i+10\right)+20,b=-5\sqrt{2}i+10$$