Solve (1)(a-2)(a-1)=a^2+1

$$( 1 ) ( a - 2 ) ( a - 1 ) = a ^ { 2 } + 1$$

Solve for a

$$a=\frac{1}{3}\approx 0.333333333$$

Steps for Solving Linear Equation

Use the distributive property to multiply 1 by a-2.

$$\left(a-2\right)\left(a-1\right)=a^{2}+1$$

Use the distributive property to multiply a-2 by a-1 and combine like terms.

$$a^{2}-3a+2=a^{2}+1$$

Subtract a^{2} from both sides.

$$a^{2}-3a+2-a^{2}=1$$

Combine a^{2} and -a^{2} to get 0.

$$-3a+2=1$$

Subtract 2 from both sides.

$$-3a=1-2$$

Subtract 2 from 1 to get -1.

$$-3a=-1$$

Divide both sides by -3.

$$a=\frac{-1}{-3}$$

Fraction \frac{-1}{-3} can be simplified to \frac{1}{3} by removing the negative sign from both the numerator and the denominator.

$$a=\frac{1}{3}$$