Datrys 6^2+(2*5+x)^2=4^2-(2*5-x)^2

$$6 ^ { 2 } + ( 2 \cdot 5 + x ) ^ { 2 } = 4 ^ { 2 } - ( 2 \cdot 5 - x ) ^ { 2 }$$

Datrys ar gyfer x (complex solution)

$$x=-\sqrt{110}i\approx -0-10.488088482i$$

$$x=\sqrt{110}i\approx 10.488088482i$$

Camau drwy Ganfod Isradd

Cyfrifo 6 i bŵer 2 a chael 36.

$$36+\left(2\times 5+x\right)^{2}=4^{2}-\left(2\times 5-x\right)^{2}$$

Lluosi 2 a 5 i gael 10.

$$36+\left(10+x\right)^{2}=4^{2}-\left(2\times 5-x\right)^{2}$$

Defnyddio'r theorem binomaidd \left(a+b\right)^{2}=a^{2}+2ab+b^{2} i ehangu'r \left(10+x\right)^{2}.

$$36+100+20x+x^{2}=4^{2}-\left(2\times 5-x\right)^{2}$$

Adio 36 a 100 i gael 136.

$$136+20x+x^{2}=4^{2}-\left(2\times 5-x\right)^{2}$$

Cyfrifo 4 i bŵer 2 a chael 16.

$$136+20x+x^{2}=16-\left(2\times 5-x\right)^{2}$$

Lluosi 2 a 5 i gael 10.

$$136+20x+x^{2}=16-\left(10-x\right)^{2}$$

Defnyddio'r theorem binomaidd \left(a-b\right)^{2}=a^{2}-2ab+b^{2} i ehangu'r \left(10-x\right)^{2}.

$$136+20x+x^{2}=16-\left(100-20x+x^{2}\right)$$

I ddod o hyd i wrthwyneb 100-20x+x^{2}, dewch o hyd i wrthwyneb pob term.

$$136+20x+x^{2}=16-100+20x-x^{2}$$

Tynnu 100 o 16 i gael -84.

$$136+20x+x^{2}=-84+20x-x^{2}$$

Tynnu 20x o'r ddwy ochr.

$$136+20x+x^{2}-20x=-84-x^{2}$$

Cyfuno 20x a -20x i gael 0.

$$136+x^{2}=-84-x^{2}$$

Ychwanegu x^{2} at y ddwy ochr.

$$136+x^{2}+x^{2}=-84$$

Cyfuno x^{2} a x^{2} i gael 2x^{2}.

$$136+2x^{2}=-84$$

Tynnu 136 o'r ddwy ochr.

$$2x^{2}=-84-136$$

Tynnu 136 o -84 i gael -220.

$$2x^{2}=-220$$

Rhannu’r ddwy ochr â 2.

$$x^{2}=\frac{-220}{2}$$

Rhannu -220 â 2 i gael -110.

$$x^{2}=-110$$

Mae’r hafaliad wedi’i ddatrys nawr.

$$x=\sqrt{110}i x=-\sqrt{110}i$$

Camau gan Ddefnyddio’r Fformiwla Cwadratig

Cyfrifo 6 i bŵer 2 a chael 36.

$$36+\left(2\times 5+x\right)^{2}=4^{2}-\left(2\times 5-x\right)^{2}$$

Lluosi 2 a 5 i gael 10.

$$36+\left(10+x\right)^{2}=4^{2}-\left(2\times 5-x\right)^{2}$$

Defnyddio'r theorem binomaidd \left(a+b\right)^{2}=a^{2}+2ab+b^{2} i ehangu'r \left(10+x\right)^{2}.

$$36+100+20x+x^{2}=4^{2}-\left(2\times 5-x\right)^{2}$$

Adio 36 a 100 i gael 136.

$$136+20x+x^{2}=4^{2}-\left(2\times 5-x\right)^{2}$$

Cyfrifo 4 i bŵer 2 a chael 16.

$$136+20x+x^{2}=16-\left(2\times 5-x\right)^{2}$$

Lluosi 2 a 5 i gael 10.

$$136+20x+x^{2}=16-\left(10-x\right)^{2}$$

Defnyddio'r theorem binomaidd \left(a-b\right)^{2}=a^{2}-2ab+b^{2} i ehangu'r \left(10-x\right)^{2}.

$$136+20x+x^{2}=16-\left(100-20x+x^{2}\right)$$

I ddod o hyd i wrthwyneb 100-20x+x^{2}, dewch o hyd i wrthwyneb pob term.

$$136+20x+x^{2}=16-100+20x-x^{2}$$

Tynnu 100 o 16 i gael -84.

$$136+20x+x^{2}=-84+20x-x^{2}$$

Tynnu -84 o'r ddwy ochr.

$$136+20x+x^{2}-\left(-84\right)=20x-x^{2}$$

Gwrthwyneb -84 yw 84.

$$136+20x+x^{2}+84=20x-x^{2}$$

Tynnu 20x o'r ddwy ochr.

$$136+20x+x^{2}+84-20x=-x^{2}$$

Adio 136 a 84 i gael 220.

$$220+20x+x^{2}-20x=-x^{2}$$

Cyfuno 20x a -20x i gael 0.

$$220+x^{2}=-x^{2}$$

Ychwanegu x^{2} at y ddwy ochr.

$$220+x^{2}+x^{2}=0$$

Cyfuno x^{2} a x^{2} i gael 2x^{2}.

$$220+2x^{2}=0$$

Ar gyfer hafaliadau cwadratig fel yr un hwn, gyda therm x^{2} ond dim term x, mae modd eu datrys drwy ddefnyddio'r fformiwla cwadratig, \frac{-b±\sqrt{b^{2}-4ac}}{2a}., unwaith y cânt eu rhoi ar ffurf safonol: ax^{2}+bx+c=0.

$$2x^{2}+220=0$$

Mae’r hafaliad hwn yn y ffurf safonol: ax^{2}+bx+c=0. Amnewidiwch 2 am a, 0 am b, a 220 am c yn y fformiwla gwadratig, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\times 220}}{2\times 2}$$

Sgwâr 0.

$$x=\frac{0±\sqrt{-4\times 2\times 220}}{2\times 2}$$

Lluoswch -4 â 2.

$$x=\frac{0±\sqrt{-8\times 220}}{2\times 2}$$

Lluoswch -8 â 220.

$$x=\frac{0±\sqrt{-1760}}{2\times 2}$$

Cymryd isradd -1760.

$$x=\frac{0±4\sqrt{110}i}{2\times 2}$$

Lluoswch 2 â 2.

$$x=\frac{0±4\sqrt{110}i}{4}$$

Datryswch yr hafaliad x=\frac{0±4\sqrt{110}i}{4} pan fydd ± yn plws.

$$x=\sqrt{110}i$$

Datryswch yr hafaliad x=\frac{0±4\sqrt{110}i}{4} pan fydd ± yn minws.

$$x=-\sqrt{110}i$$

Mae’r hafaliad wedi’i ddatrys nawr.

$$x=\sqrt{110}i x=-\sqrt{110}i$$