Question

Solve the following equations:
$\sqrt{2x^2-7x+1}-\sqrt{2x^2-9x+4}=1.$

Answer 1

Hint: Simplify the equation using the normal method by bringing common terms together on one side and then solve to find the answer.

 The given equation is as
$$\begin{gathered} \sqrt{2x^2-7x+1}-\sqrt{2x^2-9x+4}=1 \\ \Rightarrow \sqrt{2x^2-7x+1}=\sqrt{2x^2-9x+4}+1 \end{gathered}$$
 After squaring both sides, we get,
  $$\begin{gathered} 2x^2-7x+1=1+2x^2-9x+4+2\sqrt{2x^2-9x+4} \\ 2x-4=2\sqrt{2x^2-9x+4} \\ x-2=\sqrt{2x^2-9x+4} \end{gathered}$$
 Again after squaring both sides, we get,
  $$\begin{gathered} (x-2{)}^2=2x^2-9x+4 \\ {x}^2+4-4x=2x^2-9x+4 \\ {x}^2-5x=0 \\ x(x-5)=0 \\ \Rightarrow x=0,5 \end{gathered}$$
So, this is the required solution.

NOTE: On squaring the values, we must write the terms carefully, without missing any terms in between.