Datrys x^2-2x+2=(x-a)^2+b

$$x ^ { 2 } - 2 x + 2 = ( x - a ) ^ { 2 } + b$$

Datrys ar gyfer b

$$b=a\left(2x-a\right)-2x+2$$

Camau Ateb

Defnyddio'r theorem binomaidd \left(p-q\right)^{2}=p^{2}-2pq+q^{2} i ehangu'r \left(x-a\right)^{2}.

$$x^{2}-2x+2=x^{2}-2xa+a^{2}+b$$

Cyfnewidiwch yr ochrau fel bod yr holl dermau newidiol ar yr ochr chwith.

$$x^{2}-2xa+a^{2}+b=x^{2}-2x+2$$

Tynnu x^{2} o'r ddwy ochr.

$$-2xa+a^{2}+b=x^{2}-2x+2-x^{2}$$

Cyfuno x^{2} a -x^{2} i gael 0.

$$-2xa+a^{2}+b=-2x+2$$

Ychwanegu 2xa at y ddwy ochr.

$$a^{2}+b=-2x+2+2xa$$

Tynnu a^{2} o'r ddwy ochr.

$$b=-2x+2+2xa-a^{2}$$

Datrys ar gyfer a (complex solution)

$$a=\sqrt{x^{2}-2x-b+2}+x$$

$$a=-\sqrt{x^{2}-2x-b+2}+x$$

Datrys ar gyfer a

$$a=\sqrt{x^{2}-2x-b+2}+x$$

$$a=-\sqrt{x^{2}-2x-b+2}+x\text{, }b\leq x^{2}-2x+2$$