Question

what is the solution to the equation \\(sqrt3{m - 4} - sqrt3{2m + 8} = 0\\)?
\\(\circ\\) \\(m = -24\\)
\\(\circ\\) \\(m = -12\\)
\\(\circ\\) \\(m = -6\\)
\\(\circ\\) \\(m = -4\\)

Explanation:

Step1: Isolate cube roots

$\sqrt[3]{m-4} = \sqrt[3]{2m+8}$

Step2: Eliminate cube roots

$m-4 = 2m+8$

Step3: Solve for m

$m - 2m = 8 + 4$
$-m = 12$
$m = -12$

Step4: Verify solution

Substitute $m=-12$:
$\sqrt[3]{-12-4}-\sqrt[3]{2(-12)+8} = \sqrt[3]{-16}-\sqrt[3]{-16}=0$

Answer:

m = -12