Question

Solve: √8x−42= √ 21x+49. If there are multiple solutions, list them separated by a comma, e.g. 1,2. If there is no solution, enter ∅.

Answer 1

To solve the surds given, we shall begin by taking the common factors in either side of the equation, as shown below;

$\begin{gathered} \sqrt[]{8x-42}=\sqrt[]{21x+49} \\ =\sqrt[]{8x-42}=\sqrt[]{49(\frac{3}{7}x+1)} \\ =\sqrt[]{8x-42}=\sqrt[]{49}\times\sqrt[]{\frac{3}{7}x+1} \\ \sqrt[]{8x-42}=7\sqrt[]{\frac{3}{7}x+1} \\ \text{Cross multiply and you'll have} \\ \frac{\sqrt[]{8x-42}}{\sqrt[]{\frac{3}{7}x+1}}=7 \end{gathered}$

Note that there is no common factor for both radical expressions as shown in the steps above. Therefore, there is no solution for this equation.