Question

Solve for x : root of √6x+7-(2x-7)=0
the root is on 6x+7 only

Answer 1

Dear student
$$\begin{gathered} \sqrt{6\mathrm{x}+7}-\left(2\mathrm{x}-7\right)=0 \\ \Rightarrow \sqrt{6\mathrm{x}+7}=2\mathrm{x}-7 \\ \mathrm{Squaring}\mathrm{both}\mathrm{sides},\mathrm{we}\mathrm{get} \\ 6\mathrm{x}+7=4{\mathrm{x}}^2+49-28\mathrm{x} \\ \Rightarrow 4{\mathrm{x}}^2-34\mathrm{x}+42=0 \\ \Rightarrow 2{\mathrm{x}}^2-17\mathrm{x}+21=0 \\ \Rightarrow \mathrm{x}=\frac{17\pm \sqrt{{17}^2-4\left(2\right)\left(21\right)}}{2\left(2\right)} \\ \Rightarrow \mathrm{x}=\frac{17\pm \sqrt{289-168}}{4} \\ \Rightarrow \mathrm{x}=\frac{17\pm 11}{4} \\ \Rightarrow \mathrm{x}=7\mathrm{or}\mathrm{x}=\frac{3}{2} \end{gathered}$$
Regards