Question

(x-2)e2/3=49itle="(x - 2) ^{2 \div 3} = 49 " alt="(x - 2) ^{2 \div 3} = 49 " align="absmiddle" class="latex-formula">

Answer 1

$\bf (x-2)^{2\div 3}=49\implies (x-2)^{\frac{2}{3}}=7^2\implies \stackrel{\textit{raising both sides by }\frac{3}{2}}{\left( (x-2)^{\frac{2}{3}} \right)^{\frac{3}{2}}=(7^2)^{\frac{3}{2}}} \\\\\\ (x-2)^{\frac{2}{3}\cdot \frac{3}{2}}=7^3\implies (x-2)^1=7^3\implies x=7^3+2\implies x=345$