question_answer

Solve for \[x:\sqrt{6x+7}-(2x-7)=0\]

Answer:

We have, \[\sqrt{6x+7}-(2x-7)=0\]

\[\sqrt{6x+7}=(2x-7)\]

On squaring both sides

\[{{\left( \sqrt{6x+7} \right)}^{2}}={{(2x-7)}^{2}}\]

\[\Rightarrow 6x+7=4{{x}^{2}}+49-28x\]

\[\Rightarrow 4{{x}^{2}}+42-34x=0\]

\[\Rightarrow 2{{x}^{2}}-17x+21=0\]

\[\Rightarrow 2{{x}^{2}}-14x-3x+21=0\]

\[\Rightarrow 2x(x-7)-3(x-7)=0\]

\[\Rightarrow (2x-3)(x-7)=0\]

\[\Rightarrow x=\frac{3}{2}\] or \[7\]

\[\therefore \,~x=7\] (as \[x=3/2\] doesn't satisfy the given equation)