Question

Solve $x^2-2ax+(a^2-b^2)=0$.

Answer 1

Given $x^2–2ax+a^2–b^2=0$

$$\begin{gathered} \Rightarrow x^2–ax–ax+a^2–b^2=0 \\ \Rightarrow x(x-a)-a(x-a)–b^2=0 \\ \Rightarrow (x-a)(x-a)–b^2=0 \\ \Rightarrow {(x-a)}^2–b^2=0 \\ \Rightarrow (x-a-b)(x-a+b)=0 \end{gathered}$$

Either $x-a-b=0\text{or}x-a+b=0$

$\Rightarrow x=a+b\text{or}x=a-b$

Hence, $\mathit{x}\mathbf{}\mathbf{=}\mathbf{}\mathit{a}\mathbf{}\mathbf{+}\mathbf{}\mathit{b}\mathbf{}\mathbf{\text{or}}\mathit{x}\mathbf{}\mathbf{=}\mathbf{}\mathit{a}\mathbf{}\mathbf{-}\mathbf{}\mathit{b}$ is the solution of the given quadratic equation.