Question

Solving radical equations algebraically

Answer 1

`\bf \boxed{3}~\hspace{7em}√(7x-2)=√(7-6x)\implies \stackrel{\textit{squaring both sides}}{(√(7x-2))^2=(√(7-6x))^2} \\\\\\ 7x-2=7-6x\implies 13x=9\implies x=\cfrac{9}{13} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \boxed{4}~\hspace{7em}6√(x-2)=√(x+8)\implies (6√(x-2))^2=(√(x+8))^2 \\\\\\ 6^2(√(x-2))^2=x+8\implies 36(x-2)=x+8\implies 36x-72=x+8 \\\\\\ 35x=80\implies x=\cfrac{80}{35}\implies x=\cfrac{16}{7}`