Solve AB=sqrt{(a-b-a+b)^2+(a+b+b-a)^2}

$$A B = \sqrt { ( a - b - a + b ) ^ { 2 } + ( a + b + b - a ) ^ { 2 } }$$

Solve for A

$$\left\{\begin{matrix}A=\frac{2|b|}{B}\text{, }&B\neq 0\\A\in \mathrm{R}\text{, }&b=0\text{ and }B=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine a and -a to get 0.

$$AB=\sqrt{\left(-b+b\right)^{2}+\left(a+b+b-a\right)^{2}}$$

Combine -b and b to get 0.

$$AB=\sqrt{0^{2}+\left(a+b+b-a\right)^{2}}$$

Calculate 0 to the power of 2 and get 0.

$$AB=\sqrt{0+\left(a+b+b-a\right)^{2}}$$

Combine b and b to get 2b.

$$AB=\sqrt{0+\left(a+2b-a\right)^{2}}$$

Combine a and -a to get 0.

$$AB=\sqrt{0+\left(2b\right)^{2}}$$

Expand \left(2b\right)^{2}.

$$AB=\sqrt{0+2^{2}b^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$AB=\sqrt{0+4b^{2}}$$

Anything plus zero gives itself.

$$AB=\sqrt{4b^{2}}$$

The equation is in standard form.

$$BA=\sqrt{4b^{2}}$$

Divide both sides by B.

$$\frac{BA}{B}=\frac{2|b|}{B}$$

Dividing by B undoes the multiplication by B.

$$A=\frac{2|b|}{B}$$

Solve for B

$$\left\{\begin{matrix}B=\frac{2|b|}{A}\text{, }&A\neq 0\\B\in \mathrm{R}\text{, }&b=0\text{ and }A=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine a and -a to get 0.

$$AB=\sqrt{\left(-b+b\right)^{2}+\left(a+b+b-a\right)^{2}}$$

Combine -b and b to get 0.

$$AB=\sqrt{0^{2}+\left(a+b+b-a\right)^{2}}$$

Calculate 0 to the power of 2 and get 0.

$$AB=\sqrt{0+\left(a+b+b-a\right)^{2}}$$

Combine b and b to get 2b.

$$AB=\sqrt{0+\left(a+2b-a\right)^{2}}$$

Combine a and -a to get 0.

$$AB=\sqrt{0+\left(2b\right)^{2}}$$

Expand \left(2b\right)^{2}.

$$AB=\sqrt{0+2^{2}b^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$AB=\sqrt{0+4b^{2}}$$

Anything plus zero gives itself.

$$AB=\sqrt{4b^{2}}$$

Divide both sides by A.

$$\frac{AB}{A}=\frac{2|b|}{A}$$

Dividing by A undoes the multiplication by A.

$$B=\frac{2|b|}{A}$$